Prasanna

Students can Download Chapter 5 Magnetism and Matter Notes, Plus Two Physics Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus Two Physics Notes Chapter 5 Magnetism and Matter

Introduction
The word magnet is derived from the name of an island in Greece called magnesia where magnetic ore deposits were found.
Properties of a magnet

1. When a bar magnet is freely suspended, it points in the north-south direction.
2. There is a repulsive force when north poles (or south poles) are brought close together.
3. We cannot isolate the north or south pole of a magnet.
4. It is possible to make magnets out of iron and its alloys.

Note: The earth behaves as a magnet with the magnetic field pointing approximately from the geographic south to the north.

The Bar Magnet
A magnet has two poles. One pole is North pole and the other South pole.
Magnetic poles:
These two points near the ends of a magnet at which the power of attraction of the magnet is mostly concentrated are called its magnetic poles.
Note: A current carrying solenoid behaves like a bar magnet.

1. The magnetic field lines:
Properties of magnetic field lines

1. The magnetic field lines of a magnet form continuous closed loops.
2. The tangent to the field line at a given point represents the direction of magnetic field at that point.
3. Flux density of magnetic field represents the strength of magnetic field.
4. The magnetic field lines do not intersect

Field lines of bar magnet:

Field lines of current carrying solenoid:

Field lines of electric dipole:

2. Bar magnet as an equivalent solenoid:
Magnetic field along the axis of a solenoid or bar magnet

Consider a solenoid of radius ‘a’ and numberof turns per unit length‘n’. Let 2l be the length and I be the current flowing through the solenoid. Consider a point P at a distance ‘r’ from the centre of solenoid. To find magnetic field at P, we take a circular element of thickness dx at a distance x from the centre of solenoid.
The magnetic field at P due to this small element,

where ndx = N
(total number of turns in a circular element of thickness dx.)
Integrating from x = – l to x = + l, we get

If the point lies at large distance from the solenoid, we can take,
[(r – x)² + a²]^3/2 ≈ r³
r>>a, r>>x
Hence eq.(1) can be written as

Where m is called magnetic moment of the solenoid.

3. The dipole in a uniform magnetic field:
Torque acting on a magnetic dipole:
Consider a magnetic dipole of dipole moment ‘m’ placed in a uniform magnetic field B. If this dipole is rotated to an angle θ, a restoring torque will act on the needle. ie τ = -mBSinθ.
But we know rotational torque τ = la, where I is the moment of inertia of the magnetic dipole and α is the angular acceleration,
lα = -mBSinθ
(Restoring torque and rotational torque are equal in magnitude but opposite in direction)
But α = \(\frac{d^{2} \theta}{d t^{2}}\), for small rotations sinθ ≈ θ.

This equation represents that, the oscillation of this magnetic needle is simple harmonic. When we compare the above equation with standard harmonic.

Potential energy of a magnetic dipole:
The work done in rotating a magnet in a magnetic field is stored in it as its potential energy. If dipole is rotated through an angle (dθ) in a uniform magnetic field B, work done for this rotation,
dw = τdθ
dw = mBsinθdθ
If this magnetic needle is rotated from θ₁ to θ₂, total work done

If dipole is rotated from stable equilibrium (θ₁ = π/2) to θ₂ = 0 we get,
W = -mBcosθ

This work done is stored as magnetic potential energy, ie.

4. The electrostatic analog:
Permanent Magnets And Electromagnets

Substances which retain theirferromagnetic property at room temperature for a longtime, even after the magnetizing field has been removed are called permanent magnets.

The hysteresis curve helps us to select such materials. They should have high retentivity so that the magnet is strong and high coercivity so that the magnetization is not lost by strong magnetic fields. The material should have a wide hysteresis loop. Steel, Alnico, cobalt-steel and nickel are examples.

Electromagnets are usually ferromagnetic materials with low retentivity, low coercivity and high permeability. The hysteresis curve should be narrow so that the energy liberated as heat is small.
The hysteresis curves of both these materials are shown in the above figure.

Magnetism And Gauss’s Law
Gauss’s law in magnetism: The net magnetic flux through any closed surface is zero.

Explanation:

Consider a Gaussian surfaces represented by I and II. Both cases demonstrates that the number of magnetic field lines leaving the surface is balanced by the number of lines entering it. This is true for any closed surface.

The Earth’s Magnetism
Earth’s magnetic field a rise due to electrical currents produced by motion of metallic fluids in the outer core of the earth. This is known as the dynamo effect.

The magnetic field of the earth behaves as magnetic dipole located at the centre of the earth. The axis of the dipole does not coincide with the axis of rotation of the earth. The axis of dipole is titled by 11.3° with axis of rotation of the earth.

The pole near the geographic north pole of the earth is called north magnetic pole (N_m). Likewise, the pole near the geographic south pole is called the south magnetic pole. (S_m).
Note: The north magnetic pole (N_m) behaves like the south pole of a bar magnet (inside the earth). Similarly, the south magnetic pole (S_m) behaves like the north pole of a bar magnet.

(i) Magnetic declination and dip:
The elements of earth’s magnetic field:
The earth’s magnetic field at a place can be completely specified in terms of three quantities. They are

1. Declination
2. Dip
3. Horizontal intensity

Magnetic meridian:
Magnetic meridian at a place is the vertical plane passing through the earth’s magnetic poles.
Geographic meridian:
Geographic meridian at a place is the vertical plane passing through the geographic poles.

1. Magnetic Declination (I):

Declination at a place is the angle between the geographic meridian and magnetic meridian at that place.

2. Dip or Inclination (θ):

The angle between the earth’s magnetic field and the horizontal component of the earth’s magnetic field at a place is called dip. Dip angle changes from place to place. On the equator, the dip is zero and at the poles, the dip is 90°.

3. Horizontal Intensity B_h:
The horizontal intensity at a place is the horizontal components of the earths field.
Relation between Dip, Horizontal intensity and Earth’s magnetic field:

Let B be the Earth’s magnetic field and θ be the angle of dip. Let B_h be the horizontal intensity and Bvthe vertical intensity of the earth’s magnetic field. Then from figure ,we get
B_h = B cos θ
The vertical component, B_v = B sin θ
∴ Tanθ = \(\frac{B_{v}}{B_{h}}\)
and resultant field, B = \(\sqrt{\mathbf{B}_{\mathrm{h}}^{2}+\mathbf{B}_{\mathrm{v}}^{2}}\)

Magnetization And Magnetic Intensity
The magnetic properties of a substance can be studied by defining some parameter such as

1. Intensity of magnetization (M)
2. Magnetic intensity vector (H)
3. Susceptibility
4. Permeability

1. Intensity of magnetisation (M):
It is defined as the magnetic moment per unit volume. It is the measure of the extent to which a specimen is magnetized.

2. Magnetic Intensity Vector (Magnetising field):
It is defined as the magnetic field which produces an induced magnetism in a magnetic substance. If H is the magnetising field and B the induced magnetic field in the material.
ie. H = \(\frac{B}{\mu}\)
where µ is the constant called the magnetic permeability of the medium.

3. Magnetic susceptibility (χ):
Magnetic susceptibility of a specimen is the ratio of its magnetization to the magnetising field,
ie. χ = \(\frac{M}{H}\)

4. Magnetic permeability (µ):
It is the ratio of magnetic field inside a specimen to the magnetising field.
ie. µ = \(\frac{B}{H}\)
µ = µ₀µ_r
µ₀ – Permeability of free space
µ_r – Relative permeability of a medium.

Relation between permeability and susceptibility:
Let a magnetic material be kept in a solenoid. The specimen gets magnetized by induction. The resultant field inside the specimen is the sum of the field due to the current in the solenoid and the field due to the magnetization of the material.
Resultant field B = Field due to current B₀ + Field due to magnetization B_m.
∴ B = B₀ + B_m
But B_m = µ₀M, B₀ = µ₀H
∴ B = µ₀H + µ₀M

Magnetic Properties Of Materials
Materials can be classified as diamagnetic, paramagnetic or ferromagnetic in terms of the susceptibility χ. A material is diamagnetic if χ is negative, para-if χ is positive and small, and Ferro-if χ is large and positive.

1. Diamagnetism:
Diamagnetic substances are those which have tendency to move from stronger to the weaker part of the external magnetic field.
Diamagnetic material in external magnetic field:

Figure shows a bar of diamagnetic material placed in an external magnetic field. The field lines are repelled and the field inside the material is reduced.

Explanation of diamagnetism:
Electrons in an atom orbit around nucleus. These orbiting electrons produce magnetic field. Hence atom possess magnetic moment.

Diamagnetic substances are the ones in which resultant magnetic moment in an atom is zero. When magnetic field is applied, those electrons having orbital magnetic moment in the same direction slow down and those in the opposite direction speed up.

Thus, the substance develops a net magnetic moment in direction opposite to that of the applied field and hence it repels external magnetic field.

Examples:
Some diamagnetic materials are bismuth, copper, lead, silicon, nitrogen (at STP), water and sodium chloride.

Meissner effect:
The phenomenon of perfect diamagnetism in superconductors is called the Meissner effect.

2. Paramagnetism:
Paramagnetic substances are those which get weakly magnetized in an external magnetic field. They get weakly attracted to a magnet.

Reason for paramagnetism:
The atoms of a paramagnetic material possess a permanent magnetic dipole moment. But these magnetic moments are arranged in all directions.

Due to this random arrangement net magnetic moment becomes zero. But in the presence of an external field B₀, the atomic dipole moment can be made to align in the same direction of B0. Hence paramagnetic material shows magnetism in external magnetic field.
Paramagnetic material in external magnetic field:

Figure shows a bar of paramagnetic material placed in an external field. The field lines gets concentrated inside the material, and the field inside is increased.

Examples:
Some paramagnetic materials are aluminium, sodium, calcium, oxygen (at STP) and copper chloride.

Curie law of magnetism:
Curie law of magnetism states that the magnetisation of a paramagnetic material is inversely proportional to the absolute temperature T.

In the case of paramagnetic materials it can be shown that the magnetic susceptibility at temperature is given by

Where C is a constant called curie’s constant.

3. Ferromagnetism:
Ferromagnetic substances are those which gets strongly magnetized in an external magnetic field. They get strongly attracted to a magnet.
Ferro magnetic materials without external magnetic field:

The atoms in a ferromagnetic material possess a dipole moment. These dipoles align in a common direction over a macroscopic volume called domain. Each domain has a net magnetization. Domains are arranged randomly. Hence net magnetic moment of all domains is zero, so ferromagnetic substance does not show magnetism.
Ferro magnetic materials in external magnetic field:

When we apply an external magnetic field B₀, the domains arranged in the direction of B₀ and grow in size. Thus, in a ferromagnetic material the field lines are highly concentrated.

Question 1.
What happens when the external field is removed?
Answer:
In some ferromagnetic materials the magnetisation persists even if external field is removed. Such materials are called hard ferromagnets. Such materials are used to make permanent magnets.
Eg: Alnico
There is a another class of ferromagnetic materials in which the magnetisation disappears on removal of the external field. Such materials are called soft ferromagnetic materials.
Eg: soft iron

Curie temperature:
The ferromagnetic property depends on temperature. At high temperature, a ferromagriet becomes a paramagnet. The domain structure disintegrates with temperature. This disappearance of magnetisation with temperature is gradual. The temperature of transition from ferromagnetic to paramagnetism is called the Curie temperature T_c.

Variation of B and H in paramagnetic materials:
Figure shows the plot of B versus H. As H is gradually increased from zero, B also increase from zero along OP.

As H increases, more and more magnetic dipoles get aligned in the direction of the field. So M increases and hence B increases.

When all the dipoles get aligned in the direction of the field, the curve becomes almost flat. After this there is no increase of B with H.

When H is gradually decreased from P₁ there is no corresponding decrease in the magnetization. The shifting of domains in the ferromagnetic materials is not completely reversible and some magnetization remains even when H is reduced to zero.

The value of the magnetic field when H is zero is called the remanent field Br (Retentivity). If the current in the solenoid is now reversed so that H is in the opposite direction, the magnetic field B can be gradually brought to zero at the point C. The value of H needed to reduce B to zero is called the coercive force He (Coercivity).

The remaining part of curve is obtained by applying H in reverse direction. From these variations it is clear that B always lags behind H. This phenomenon is known as magnetic hysteresis (hysteresis means to lag behind).

The area enclosed by the hysteresis curve gives the loss of energy in the form of heat during the magnetisation – demagnetization cycle.

Permanent Magnets And Electromagnets

Substances which retain theirferromagnetic property at room temperature for a longtime, even after the magnetizing field has been removed are called permanent magnets.

The hysteresis curve helps us to select such materials. They should have high retentivity so that the magnet is strong and high coercivity so that the magnetization is not lost by strong magnetic fields. The material should have a wide hysteresis loop. Steel, Alnico, cobalt-steel and nickel are examples.

Electromagnets are usually ferromagnetic materials with low retentivity, low coercivity and high permeability. The hysteresis curve should be narrow so that the energy liberated as heat is small.
The hysteresis curves of both these materials are shown in the above figure.

Students can Download Chapter 4 Moving Charges and Magnetism Notes, Plus Two Physics Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus Two Physics Notes Chapter 4 Moving Charges and Magnetism

Introduction; Oersted Experiment
The magnetic effect of current was discovered by Danish Physicist Hans Christians Oersted. He noticed that a current in a straight wire makes a deflection in a magnetic needle.

The deflection increases on increasing current. He also found that reversing the direction of current reverses direction of needle. Oersted concluded that current produces a magnetic field around it.

Magnetic Force
1. Sources and fields:
The static charge is the source of electric field. The source of magnetic field is current or moving charge. Both the electric and magnetic fields are vector fields and both obeys superposition principle.

2. Lorentz Force:
The force experienced by moving charge in electric and magnetic field is called Lorentz force. The Lorentz force experienced by charge ‘q’ moving with velocity ‘v’, is given by

= F_electric + F_magnetic
The features of Lorentz Force:

1. The Lorentz force on positive charge is opposite to that on negative charge because it depends on charge ‘q’.
2. The direction of Lorentz force is perpendicular to velocity and magnetic field. Its direction is given by screw rule or right hand rule.
3. Only moving charge experiences magnetic force. For static charge (v = 0), magnetic force is zero.

Note:

1. A charge particle moving parallel or antiparallel to magnetic field will not experience magnetic force and moves undeviated.
2. The work done by magnetic force is zero. Because magnetic force is always perpendicular to direction of velocity.
3. A charged particle entering perpendicular magnetic field (θ = 90°) will make a circular path.
4. The unit of B is Tesla.

3. Magnetic force on current carrying conductor:
Consider a rod of uniform cross section ‘A’ and length ‘e’. Let ‘n’ be the number of electrons per unit volume (number density). ‘v_d’ be the drift velocity of electrons for steady current ‘I’.
Total number of electrons in the entire volume of rod = nAl
Charge of total electrons = nA l.e
‘e’ is the charge of a single electron.
The Lorentz force on electrons,

(I = neAV_d)

Motion In Magnetic Field
Case I:
The charged particle enters perpendicular to magnetic field.(\(\overrightarrow{\mathrm{V}}\) is perpendicular to \(\overrightarrow{\mathrm{B}}\))
When charged particle moves perpendicular to magnetic field, it experiences a magnetic force of magnitude, qVB and the direction of the force is perpendicular to both \(\overrightarrow{\mathrm{B}}\) and \(\overrightarrow{\mathrm{V}}\). This perpendicular magnetic field act as centripetal force and charged particle follows a circular path.

Mathematical explanation:
Let a charge ‘q’ enters into a perpendicular magnetic field B with velocity V. Let r be the radius of circular path. The centripetal force for charged particle is provided by magnetic force.

Thus radius of circle described by charged particle depends on momentum, charge and magnetic field. If ω is the angular frequency
ω = \(\frac{v}{r}\)
Thus from (1) we get

The frequency ν = \(\frac{q B}{2 \pi m}\)
Thus frequency of revolution of charge is independent of velocity (and hence energy)
The time period T = \(\frac{2 \pi \mathrm{m}}{\mathrm{qB}}\)
(ν = \(\frac{1}{T}\)).

Case II:
The charged particles enters at an angle ‘θ’ with magnetic field.
Since the charged particle enters at an angle ‘θ’ with magnetic field, its velocity will have two components; a component parallel to magnetic field, V_॥ (Vcosθ) and a component perpendicular to the magnetic field, V_⊥(Vsinθ).

The parallel component of velocity remains unaffected by magnetic field and it causes charged particle to move along the field.

The perpendicular component makes the particle to move in circular path. The effect of linear and circular movement produce helical motion.

Pitch and Helix: The distance moved along magnetic field in one rotation is called pitch ‘P’

The radius of circular path of motion is called helix.

Motion In Combined Electric And Magnetic Fields
1. Velocity selector:
A transverse electric and mag¬netic field act as velocity selector. By adjusting value of E and B, it is possible to select charges of particular velocity out of a beam containing charges of different speed.

Explanation:
Consider two mutually perpendicular electric and magnetic fields in a region. A charged particle moving in this region, will experience electric and magnetic force. If net force on charge is zero, then it will move undeflected. The mathematical condition for this undeviation is

The charges with this velocity pass undeflected through the region of crossed fields.

2. Cyclotron
Uses: It is a device used to accelerate particles to high energy.
Principles: Cyclotron is based on two facts

1. An electric field can accelerate a charged particle.
2. A perpendicular magnetic field gives the ion a circular path.

Constructional Details:
Cyclotron consists of two semicircular dees D₁ and D₂, enclosed in a chamber C. This chamber is placed in between two magnets. An alternating voltage is applied in between D₁ and D₂. An ion is kept in a vacuum chamber.

Working:
At certain instant, let D₁ be positive and D₂ be negative. Ion (+ve) will be accelerated towards D₂ and describes a semicircular path (inside it). When the particle reaches the gap, D₁ becomes negative and D₂ becomes positive. So ion is accelerated towards D₁ and undergoes a circular motion with larger radius. This process repeats again and again.

Thus ion comes near the edge of the dee with high K.E. This ion can be directed towards the target by a deflecting plate.

Mathematical expression:
Let V be the velocity of ion, q the charge of the ion and B the magnetic flux density. If the ion moves along a semicircular path of radius ‘r’, then we can write

[Since θ =90°, B is perpendicular to v]
or v = \(\frac{q B r}{m}\) _____(1)
Time taken by the ion to complete a semicircular path.

Eq. (2) shows that time is independent of radius and velocity.

Resonance frequency (cyclotron frequency):
The condition for resonance is half the period of the accelerating potential of the oscillator should be ‘t’. (i.e.,T/2 = t or T = 2t). Hence period of AC
T = 2t

K.E of positive ion

Thus the kinetic energy that can be gained depends on mass of particle charge of particle, magnetic field and radius of cyclotron.
Limitations:

1. As the particle gains extremely high velocit, the mass of particle will be changed from its constant value. This will affect the normal working of cyclotron as frequency depends of mass of particle.
2. Very small particles like electron can not be accelerated using cyclotron. This is because as the mass of electron is very small the cyclotron frequency required becomes extremely high which is practically difficult.
3. Neutron can’t be accelerated

Magnetic Field Due To Current Element; Biot Savart Law

The magnetic field at any point due to an element of current carrying conductor is

1. Directly proportional to the strength of the current (I)
2. Directly proportional to the length of the element (dl)
3. Directly proportional to the sine of the angle (θ) between the element and the line joining the midpoint of the element to the point.
4. Inversely proportional to the square of the distance of the point from the element

The direction of magnetic field is perpendicularto the plane containing d/and rand is given by right hand screw rule.
In the above expression \(\frac{\mu_{0}}{4 \pi}\) is the constant of proportionality and µ₀ is called the permeability of vacuum. Its value is 4π × 10^-7 TmA^-1.
Note: A magnetic field acting perpendicularly in to the plane of the paper is represented by the symbol ⊗ and a magnetic field acting perpendicularly out of the paper is represented by the symbol ⵙ.

Comparison between Biot-Savart Law and Coulomb’s law
Similarities:

1. The two laws are based on inverse square of distance and hence they are long range.
2. Both electrostatic and magnetic fields obey superposition principle.
3. The source of magnetic field is linear; (the current element \(\overrightarrow{\mathrm{ldl}}\)). The source of electrostatic force is also linear; (the electric charge).

Differences:

Magnetic Field On The Axis Of A Circular Current Loop

Consider a circular loop of radius ‘a’ and carrying current ‘I’. Let P be a point on the axis of the coil, at distance x from A and r from ‘O’. Consider a small length dl at A. The magnetic field at ‘p’ due to this small element dl,

\(\mathrm{dB}=\frac{\mu_{0} \mathrm{Idl}}{4 \pi \mathrm{x}^{2}}\) _____(1)
[since sin 90° – 1]
The dB can be resolved into dB cosΦ (along Py) and dB sinΦ (along Px).
Similarly consider a small element at B, which produces a magnetic field ‘dB’ at P. If we resolve this magnetic field we get.
dB sinΦ (along px) and dB cosΦ (along py¹)
dB cosΦ components cancel each other, because they are in opposite direction. So only dB sinΦ components are found at P, so total filed at P is

but from ∆AOP we get, sinΦ = a/x
∴ We get

Point at the centre of the loop: When the point is at the centre of the loop, (r = 0)
Then,

1. Magnetic field at the centre of loop:
The magnetic field at a distance x from centre of loop is given by

The direction of magnetic field due to current carrying circular loop is given by right hand thumb rule.

Thumb Rule: Curl of palm of right hand around circular coil with fingers pointing in the direction of current. Then extended thumb gives the direction of magnetic field.

Note:

1. An anticlockwise current gives a magnetic field out of the coil and a clockwise current gives a magnetic field into the coil.
2. The current carrying loop is equivalent to magnetic dipole of dipole moment m = IA

Ampere’s Circuital Law
According to ampere’s law the line integral of magnetic field along any closed path is equal to µ₀ times the current passing through the surface.

Applications Of Ampere’s Circuital Law
1. Long straight conductor:
Consider a long straight conductor carrying T ampere current. To find magnetic field at ‘P’, we construct a circle of radius r (passing through P).

According to Ampere’s circuital law we can write

[B and dl are parallel]
B∫dl = µ₀I
B2πr = µ₀I
B = \(\frac{\mu_{0} I}{2 \pi r}\)

2. Magnetic field due to long solenoid:

Consider a solenoid having radius T. Let ‘n’ be the number of turns per unit length and I be the current flowing through it.
In order to find the magnetic field (inside the solenoid) consider an Amperian loop PQRS. Let V ‘ be the length and ‘b’ the breadth
Applying Amperes law, we can write

Substituting the above values in eq (1),we get
Bl = µ₀ l_enc ____(2).
But l_enc = n l I
where ‘nl ’ is the total number of turns that carries current I (inside the loop PQRS)
∴ eq (2) can be written as
Bl = µ₀ nIl
B = µ₀nI
If core of solenoid is filled with a medium of relative permittivity µ_r. then
B = µ₀µ_rnl

3. The toroid:
Consider a toroid of average radius ‘r’. Let ‘n’ be the number of turns per unit length. Let I be the current flowing through the toroid. In order to find magnetic field inside the toroid, an camperian loop of radius ‘r’ is considered.

Applying Amperes law to the loop, we can write

Where ‘n2πr ‘ is the total number of turns of the solenoid that carries current I (inside the Amperian loop) Integrating the eq(1) we get
B 2πr = µ₀2πrI
B = µ₀n I
If the core of the solenoid is filled with a medium of relative permeability µ_r then the above equation is modified as

Note: The magnetic field due to toroid is same as that due to solenoid.

Force Between Two Parallel Currents, The Ampere Force Between Two Parallel Conductors

P and Q are two infinitely long conductors placed parallel to each other and separated by a distance r, Let the current through P and Q be l₁ and l₂ respectively.
Magnetic field at a distance ‘r’ from P is

Conductor ‘Q’ is placed in this magnetic field.
If l₂ is the length of the conductor ‘Q’, the Lorentz force on ‘Q’ is

∴ Force per unit length can be written as,

Where f = \(\frac{F}{\ell_{2}}\)
Note:

1. When currents are in the same direction, the force is attractive
2. If the currents are in the opposite direction, the force is repulsive.

Definition of ampere:
An ampere is defined as that constant current which if maintained in two straight parallel conductors of infinite lengths placed one meter apart in vacuum will produce between a force of 2 × 10^-7 Newton per meter length.

Force On A Current Loop, Magnetic Dipole
1. Torque on a rectangular current loop in uniform magnetic filed:

Considers rectangular coil PQRS of N turns which is suspended in a magnetic field, so that it can rotate (about yy 1). Let ‘l’ be the length (PQ) and ‘b’ be the breadth (QR).

When a current l flows in the coil, each side produces a force. The forces on the QR and PS will not produce torque. But the forces on PQ and RS will produce a Torque.
Which can be written as
τ = Force × ⊥ distance _______(1)
But, force = BlI ______(2)
[since θ = 90° ]
And from ∆QTR , we get
⊥ distance (QT) = b sin θ ______(3)
Substituting the vales of eq (2) and eq (3) in eq(1) we get
τ = BIl b sin θ
= BIA sin θ [since lb = A (area)]
τ = IAB sin θ
τ = mB sin θ [since m = IA]

If there are N turns in the coil, then
τ = NIAB sin θ

2. Circular Current loop as a magnetic di pole:
Current loop of any shape act as magnetic dipole.
Current loop acts as magnetic dipole:
The magnetic field due to circular loop of radius R carrying current I at a distance ‘x’ from the centre of loop (on the axis of loop) is given by,

The magnetic field at large distance (x>>R) on axis of loop is

Dividing and multiplying by π

Comparison of magnetic dipole and electric dipole:
The equation (1) is similar to electric field due to electric dipole at a distance ‘x’ from the centre of dipole on its axial line.

Comparing eq(1) and (2), we get 1

m → P
B → E
From this comparison it is clear that a circular current loop acts as a magnetic dipole.

3. The magnetic dipole moment of a revolving electron:
According to Bohr’s model of atom, electrons are revolving around nucleus in its orbit. The electron revolving in its orbit can be considered as circular current loop.

Consider an electron of charge e, revolving around nucleus of charge +ze as shown in figure. The uniform, circular motion of electron constitute current ‘I’. If T is the period of revolution e
I = \(\frac{e}{T}\) _____(1)
If r is the radius of orbit and V s the orbital speed then
T = \(\frac{2 \pi r}{v}\)
Substituting this in (1), we get
I = \(\frac{e v}{2 \pi r}\)
The magnetic moment associated orbiting electron is denoted by µ₁

A = πr², area of orbit
Dividing and multiplying by m_e (Mass of electron)

Applying Quantum Theory, Bohr has proposed that angular momentum of electron can take only discrete values given by,
l = \(\frac{\mathrm{nh}}{2 \pi}\) (Bohr’s quantization condition where n = 1, 2, 3, ……..etc) where h is Plank’s constant. Thus

The orbital magnetic moment of electron is given by

Bohr Magneton: We get the minimum value of magnetic moment, when n = 1 ie

(when n = 1)
Its value is 9.27 × 10^-24 Am². This is called Bohr magneton.
Gyromagnetic Ratio:
The orbital magnetic moment of electron is related to orbital angular momentum ‘l’ as

The ratio of orbital magnetic moment to orbital angular momentum is constant. This constant is called gyromagnetic ratio. Its value is 8.8 × 10¹⁰ c/kg for an electron.

The Moving Coil Galvanometer
It is an instrument used to measure small current.
Principle: A conductor carrying current when placed in a magnetic field experiences a force, (given by Fleming’s left hand rule).
Construction:

A moving coil galvanometer consists of rectangular coil of wire having area ‘A’ and number of turns ‘n’ which is wound on metallic frame and is placed between two magnets. The magnets are concave in shape, which produces radial field.

Working: Let ‘l’ be the current flowing the coil, Then the torque acting on the coil.
τ = NIAB Where A is the area of coil and B is the magnetic field.
This torque produces a rotation on coil, thus fiber is twisted and angle (Φ). Due to this twisting a restoring torque (τ = KΦ) is produced in spring.
Under equilibrium, we can write
Torque on the coil = restoring torque on the spring
or NIAB = kΦ
or Φ = (\(\frac{\mathrm{BAN}}{\mathrm{K}}\))I
The quantity inside the bracket is constant for a galvanometer.
Φ α I
The above equation shows that the deflection depends on current passing through galvanometer.

1. Ammeter and voltmeter:
For measuring large current, the galvanometer can be converted in to ammeter and voltmeter.
Ammeter:
Ammeter is an instrument used to measure current in the circuit.

A galvanometer can be converted into an ammeter by a low resistance (shunt) connected parallel to it.

Theory:
Let G be the resistance of the galvanometer, giving full deflection fora current Ig.

To convert it into an ammeter, a suitable shunt resistance ‘S’ is connected in parallel. In this arrangement Ig current flows through Galvanometer and remaining (I – Ig) current flows through shunt resistance.
Since G and S are parallel
P.d Across G = p.d across
Ig × G = (I – Ig)S

Connecting this shunt resistance across galvanometer we can convert a galvanometer into ammeter.

2. Conversion of galvanometer into voltmeter:
To convert a galvanometer into a voltmeter, a high resistance is connected in series with it.

Theory:
Let Ig be the current flowing through the galvanometer of resistance G. Let R be the high resistance co connected in series with G.

From figure we can write
V = IgR + IgG
V – IgG = IgR

Using this resistance we can covert galvanometer in to voltmeter.

Current sensitivity:
The current sensitivity of galvanometer is the deflection produced by unit current.

The current sensitivity can be increased by increasing number of turns.

The voltage sensitivity:
The voltage sensitivity of galvanometeris the deflection produced by unit voltage.

The increase in number of turns will not change voltage sensitivity.
When number of turns double (N → 2N), the resistance of the wire will be double (ie. R → 2R). Hence the voltage sensitivity does not change.

Students can Download Chapter 8 The d and f Block Elements Notes, Plus Two Chemistry Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus Two Chemistry Notes Chapter 8 The d and f Block Elements

The d-block (Transition elements) – elements of the groups 3 – 12 in which the d-orbitals are progressively filled. The f-block (Inner transition elements) – elements in which the 4f and 5f orbitals are progressively filled.

The Transition Elements (d-block):
Their position is in between more electropositive s-block and more electronegative p-block elements.

General Electronic Configuration:
(n -1) d^1-10ns^1-2
The transition metals are classified as,

1. 3d series – 1^st transition series (Sc – Zn)
2. 4d series – 2^nd transition series (Y – Cd)
3. 5d series – 3^rd transition series (La, Hg – Hg)
4. 6d series – 4^th transition series (Ac, Rf – Cn)

Pseudo transition elements – Zn, Cd and Hg are not regarded as transition elements because their orbitals are completely filled in the ground state as well as in their common oxidation states, [(n – 1)d¹⁰ns²]. But they included in transition series due to some similarity to transition metals.

General Properties of Transition Elements:
1. Physical Properties:
High tensile strength, ductility malleability, high thermal and electrical conductivity and metallic lustre, very much hard and low volatile (except Zn, Cd and Hg), high mp (due to interatomic metallic bonding) and bp.

2. Variation in Atomic and Ionic Sizes:
Decreases with increasing atomic number because the new electron enters a d-orbital with low shielding power.

3. Ionisation Enthalpies:
Due to an increase in nuclear charge which accompanies the filling of the inner d-orbitals, there is an increase in ionisation enthalpy along the series.

First ionisation potential/enthalpy of the 5d series are higher than those of the 3d and 4d metals. This is due to lanthanoid contraction caused by poor shielding of the 4f electrons.

4. Oxidation State:
Transition elements shows various oxidation states which aries due to incomplete filling of d-orbital. The elements which give the greatest number of oxidation state occur in or near the middle of the series, e.g. Mn (+2 to +7)

5. Trends in the M²⁺/M Standard Electrode Potential:
The general trend towards less negative E° values across the series is related to the general increase in the sum of the first and second ionisation enthalpies.

6. Trends in Stability of Higher Oxidation State:
In halides, the ability of fluorine to stabilise the highest oxdn. state is due to either higher lattice energy or higher bond enthalpy. The stability of Cu²⁺(aq) rather than Cu⁺(aq) is due to the much more negative Δ_hydH° of Cu²⁺(aq) than Cu⁺(aq).

7. Chemical Reactivity:
Many of them are sufficiently electropositive to dissolve in mineral acids, a few are unaffected by simple acids. The metals of the first series are relatively more reactive and are oxidised by 1M H⁺ (except Cu).

8. Magnetic Properties:
(a) Diamagnetism:
Due to paired electrons, they are weakly repelled by applied magnetic field.

(b) Paramagnetism:
Due to presence of unpaired electrons paramagnetic substances are weakely attracted by applied magnetic field.

(c) Ferromagnetic:
Extreme form of paramagnetism, very strongly attracted by magnetic field. For transition elements, the magnetic moment is determined by the number of unpaired electrons and is calculated by spin-only formula,
\(\mu=\sqrt{n(n+2)}\)
where n is the number of unpaired electrons. The unit is Bohr magneton (BM). e.g.

9. Formation of Coloured Ions:
Most of the transition metal ions are coloured due to d-d transition of electrons. When an electron from a lower energy d orbital is excited to a higher energy d orbital, the energy of excitation corresponds to the frequency of light absorbed. The colour observed corresponds to the complementary colour of the light absorbed,

Example:

1. 1. • Sc³⁺(3d°), Ti⁴⁺ (3d°), Zn²⁺ (3d¹⁰) – Colourless
      • Ti³⁺ (3d¹) – Purple
      • Mn²⁺ (3d⁵) – Pink
      • Fe²⁺ (3d⁶) – Yellow
      • Fe³⁺ (3d⁵) – Green.

10. Formation of Complex Compounds:
They can form a large number of complex compounds due to the comparatively smaller sizes of the metal ions, their high ionic changes and the availability of d- orbital for bond formation.

(a) Catalytic Properties:
It is due to their ability to adopt multiple oxidation states and to form complexes, eg: V₂O₅ (Contact process), Fe (Haber’s process), Ni/Pt/Pd (Hydrogenation of hydrocarbon), TiCl₄ & Al(C₂H₅)₃ (Zeigler – Natta catalyst – polymerisation of ethene and propene).

11. Formation of Interstitial Compounds:
They are formed when small atoms like H, C or N are trapped inside the crystal lattices of metals. They hey are non-stoichiometric and are neither ionic nor covalent.

Characteristics – high m.p, very hard, retain metallic conductivity, chemically inert.

12. Alloy Formation:
Due to similar radii, they form alloys very easily.

Some Important Compounds of Transition Elements:
(a) Potassium Dichromate (K₂Cr₂O₇):
Obtained by the fusion of chromite ore (K₂Cr₂O₄ with Na/K₂CO₃ in pressure of air.

4FeCr₂O₄ + 8Na₂CO₃ + 7O₂ → 8Na₂CrO₄ + 2Fe₂O₃ + 8CO₂

The yellow solution of sodium chromate is filtered and acidified with H₂SO₄ to give orange sodium di chromate.

2Na₂CrO₄ + 2H⁺ → Na₂Cr₂O₇ + H₂O
Na₂Cr₂O₇ is converted into K₂Cr₂O₇ by adding KCl.
Na₂Cr₂O₇ + 2KCl → K₂Cr₂O₇ + 2NaCl

The chromate and dichromate are interconvertible in aqueous solution depending upon P^H of the solution.
2CrO₄^2- + 2H⁺ → Cr₂O₂^2- + H₂O
CrO₇^2- + 2OH^– → 2CrO₄^2- + H₂O

Uses:
K₂/Na₂Cr₂O₇-strong oxidising agents. Na₂Cr₂O₇ used in organic chemistry due to its greater solubility. K₂Cr₂O₇ is used as primary standard in volumetric analysis. Oxidising action in acidic.
solution:
Cr₂O₂^2- + 14H⁺ + 6e^– → 2Cr³⁺ + 7H₂O
e.g. It oxidises l^– to l₂, S^2- to S, Sn²⁺ to Sn⁴⁺ and Fe²⁺ to Fe³⁺

(b) Pottassium Permanganate (KMnO₄):
Preparation:
By the fusion of pyrolusite ore (MnO₂) with KOH and oxidising agent like KNO₃to give dark green K₂MnO₄ which disproportionates in a neutral or acidic solution to give KMnO₄.

2MnO₂ + 4KOH + O₂ → 2K₂MnO₄ + 2H₂O
3MnO₄^2- + 4H⁺ → 2MnO₄^– + MnO₂ + H₂O

Commercial preparation:
By the electrolytic oxidation of MnO₄^2- ion (Manganate ion).

Laboratory preparation:
By oxidising Mn²⁺ salt using peroxodisulphate.
2Mn²⁺ + 5S₂O₈^2- + 8H₂O → 2MnO₄^– + 10SO₄^2- + 16H^–

Properties:
Dark purple colour, isostructural with KClO₄, on heating decomposes at 513 K
(2KMnO₄ → K₂MnO₄ + MnO₂ + O₂).
It has temperature dependent paramagnetism. Manganate ion – green, paramagnetic (one unpaired electron). Permanganate ion – purple, diamagnetic. The manganate and permanganate ions are tetrahedral.

Acidified permanganate solution oxidises oxalates to CO₂, Fe²⁺ to Fe³⁺, NO₂^– to N03^–, I^– to I₂, S^2- to S, SO₃^2- to SO₄^2-.

Uses:
In analytical chemistry; in organic chemistry as oxidising agent; for bleaching wool, cotton, silk and other textile fibres; fordecolourisation of oils.

The Inner Transition Elements (f-block):
It consist of the two series, lanthanoids (the 14 elements following La) and actinoids (the 14 elements following Ac).

The Lanthanoids:
1. General Electronic Configuration:
(n – 2) f^1-14(n-1)d^0-1ns²

2. Atomic and Ionic Sizes:
There is a regular (steady) decrease in the size of atoms/ions with increase in atomic number as we move across from La to Lu. This slow decrease in size is known as lanthanoid contraction.

(a) Cause of Lanthanoid Contraction:
The 4f electrones constitute inner shells and are ineffective in screening the nuclear charge. Consequently, the attraction of the nucleus for the electrones in the outer most shell increases with increase in atomic number and the electron cloud shrinks. As a result, the size of the lanthanoids decreases.

Consequences:
(a) Similarity of second and third transition series:
The atomic radii of 2^nd row transition series are almost similar to those of third row transition series. Zrand Hf have almost similar radii. This makes it difficult to separate the elements in the pure state.

(b) Variation in the basic strength of hydroxides:
The size of M³⁺ ion decreases and covalent character M-OH increases. OH^– ions are not easily released. Hence the basic strength of oxides and hydroxides decrease from lanthanum to lutetium.

3. Oxidation States:
They display variable oxidation state. The most stable oxidaiton state is +3. They also show +2 and +4 oxidaiton states.

4. General Characteristics:
Due to f-f transition, they form coloured ions. They form carbides when heated with carbon, liberates H₂ from dilute acids, form halides, oxides and hydroxides, form alloys, e.g. Misch metal.

Actinoids:
14 elements from Th to Lr, radio active, most of the elements are man made.

1. Electronic configuration-similar to Lanthanoids, but the last electron is filled in 5f – orbital.

2. Ionic Sizes:
The gradual decrease in the size of the atoms or ions across the series (actinoid contraction). It is greater because of poor shielding by 5f electrons.

3. Oxidation States:
Common +3 oxidation state, also show +4, +5, +6, +7. But +3 and +4 ions tend to hydrolyse.

4. General Characteristics and Comparison with Lanthanoids:
Highly reactive metals. HCl acid attacks all metals, alkalies have no action, magnetic properties are more complex than those of lanthanoids.

Application of d- and f-block Elements:
Iron and steels-most important construction materials, TiO- used in pigment industry, MnO₂ – used in dry battery cells. Battery industry also requires Zn and Ni/Cd. Cu, Ag and Au – coinage metals.

Metals and metal compounds – essential catalysts.
PdCl₂ – used in Wacker Process
AgBr -used in photography.

Students can Download Chapter 4 Determinants Notes, Plus Two Maths Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus Two Maths Notes Chapter 4 Determinants

Introduction
Determinants have wide applications in engineering, Science, Economics, Social Science, etc. In this chapter we study about the various properties of determinants, minors, cofactors, applications in finding the area of triangle, adjoint, and inverse of a square matrix, and consistency and in consistency of linear equations.

A. Basic Concepts
I. Determinant
Determinant is a real number associated with a square matrix. The determinant of matrix A is denoted by |A|. The value of a determinant is obtained by the sum of products of elements of a row (column) with corresponding cofactors.

• |AB| = |A||B|
• |Aⁿ| = |A|ⁿ

Properties:
(i) The value of a determinant remains the same if its rows and columns are interchanged.
ie; |A^T| = |A|.

(ii) If any two rows (or columns) of a determinant are interchanged, then sign of determinant changes.

(iii) If any two rows (or columns) of a determinant is identical, then value of determinant is zero.

(iv) If each element of a row (or columns) of a determinant is multiplied by a constant k, then its value gets multiplied by k.

(a) If A is a square matrix of order n, then
|KA| = kⁿ|A|

(v) If any two rows (or columns) of a determinant is proportional, then value of determinant is
zero.

(vi) If some or all elements of a row or column of a determinant are expressed as sum of two (or more) terms, then the determinant can be expressed as sum of two (or more) determinants.

(vii) If, to each element of any row or column of a determinant, the equimultiples of corresponding elements of other row (or column) are added, then value of determinant remains the same, ie; the value of determinant remains same if we apply the operation R_i → R_i + kR_j or C_i → C_i + kC_j.

(viii) If the elements of a row or column are multiplied with cofactors of any other row or column, then their sum is zero.
ie; for example; a₁₁C₂₁ + a₁₂C₂₂ + a₁₃C₂₃ = 0.

If the elements of a row or column are multiplied with cofactors of the corresponding row or column, then their sum is |A|.
ie; for example; a₁₁C₁₁ + a₁₂C₁₂ + a₁₃C₁₃ = |A|.

1. Minor of an element:
The minor of an element a_ij is the determinant obtained by deleting the ith row and jth column, usually denoted by M_ij.

2. Cofactor of an element:
A signed Minor is called cofactor, ie; C_ij = (-1 )^{i + j} M_ij. The matrix obtained by replacing all elements by its cofactor is called cofactor matrix.

3. Adjoint Matrix:
The transpose of a cofactor matrix is. called Adjoint Matrix, usually denoted by adj(A)

Properties:

• A × adj(A) = adj(A) × A = I|A|
• If A is a square matrix of order n, then |adj(A)| = |A|^{n – 1}
• adj(AB) = adj(A)adj(B)

II. Inverse of a Matrix
A square matrix A is invertible if |A| ≠ 0 and A inverse is denoted by A^-1 ie; A^-1 = \(\frac{a d j(A)}{|A|}\)
Properties:

• (A^-1)^-1 = A
• (AB)^-1 = B^-1A^-1
• (A^T)^-1 = (A^-1)^T
• If A is a square matrix of order n, then adj(adj(A)) = |A|^n-2 × A.

III. Application of Determinants
1. Area of a triangle whose vertices are (x₁, y₁), (x₂, y₂), (x₃, y₃) is

(i) If Area = 0 then the points are collinear.

2. Solving of system of linear equations using
matrix method:
Consider the system of linear equations
a₁x + b₁y + C₁z = d₁
a₂x + b₂y + c₂z = d₂
a₃x + b₃y + c₃z = d₃
Convert the linear equation into matrix form AX = B, where

Then the solution is given by X = A^-1B

• If |A| ≠ 0 the system is consistent and has unique solution.
• If |A| = 0 and adj(A) × B ≠ 0,the system is inconsistent and has no solution.
• If |A| = Oandadj(A) × B = 0 ,the system may be consistent and has infinitely many solutions.

In order to find these infinitely many solutions, replace one of the variable by k (say z = k) and solve any two of the given equations for x and y in terms of k

Students can Download Chapter 3 Matrices Notes, Plus Two Maths Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus Two Maths Notes Chapter 3 Matrices

Introduction
The term ‘matrix’ was first used in 1850 by the famous English Mathematician James Joseph Sylvester. In 1858 Arther Cayley began the Systematic development of the theory of matrices. Matrix was first used for the study of linear equations and linear transformations. Now it is largely used in disciplines like statistics, physics, chemistry, psychology, etc.

A. Basic Concepts
I. Matrix
A matrix is an ordered rectangular array of numbers or functions. The numbers or functions are called the elements or the entries of the matrix.
1. Order of a Matrix:
A matrix having m rows and n column is called a matrix of order m × n, generally denoted by

Where 1 ≤ i ≤ m, 1 ≤ j ≤ n  i, j ∈ N.

II. Types of Matrix

• Column Matrix: A matrix having only one column is called Column Matrix.
• Row Matrix: A matrix having only one row is called Row Matrix.
• Square Matrix: A matrix having equal number of row and column is called Square Matrix.
• Diagonal Matrix: A Square matrix having all its non-diagonal entries zero is called Diagonal Matrix.
• Scalar Matrix: A Square matrix having all its non-diagonal entries zero and equal diagonal elements is called Scalar Matrix.
• Identity Matrix: A Square matrix having all its non-diagonal entries zero and diagonal elements unity is called an Identity Matrix.
• Zero Matrix: A matrix having all elements zero is called Zero Matrix.

III. Operations on matrices
1. Equality of Matrices:
Two matrices are equal if they are of same order and corresponding elements are equal.

2. Addition:
Addition is possible only if the two matrices are of same order and the operation is done by adding the corresponding elements in each Matrix. The addition of Matrix A and B is denoted by A + B.
Properties:

• Matrix addition is Commutative.
• Matrix addition is Associative.
• Zero Matrix is the additive identity.
• – A is the additive inverse of matrix A.

3. Scalar Multiplication:
The multiplication of a matrix by a scalar number k is done by multiplying each entries of A by k and matrix thus obtained is kA.

4. Difference:
Difference is possible only if the two matrices are of same order and the operation is done by subtracting the corresponding elements in each Matrix. The difference of Matrix A and B is denoted by A – B.

5. Multiplication:
Multiplication is possible only if the number of column of first matrix is equal to the number of rows of the second. The operation is done by multiplying the element in the first row of the first matrix with the corresponding elements in the first column in the second matrix.

This is continued till the rows in the first matrix finish. The multiplication of Matrix A and B is denoted by A × B or AB.
Properties:

• Matrix multiplication is Non-Commutative.
• Matrix multiplication is Associative, le; A(BC) = (AB)C
• Matrix multiplication is Distributive over addition, ie; A(B + C) = AB + AC
• Identity Matrix is the multiplicative identity, le; AI = IA.

IV. Transpose of a Matrix
The transpose of a matrix A is obtained by interchanging the row and column of A and is denoted by A^T.
Properties:

• [A^T]^T = A
• [kA]^T = kA^T
• [A + B]^T = A^T + B^T
• [AB]^T = B^T A^T

1. Symmetric Matrix:
A square matrix is said to be symmetric if [A]^T = A.
Properties:
In a symmetric matrix the corresponding elements on both sides of the main diagonal will be same.

2. Skew Symmetric Matrix:
A square matrix is said to be symmetric if [A]^T = -A.
Properties:

• In a Skew Symmetric matrix the corresponding elements on both sides of the main diagonal differ only in sign.
• For any square matrix A with real entries, A + A^T is Symmetric matrix, and A – A^T is Skew Symmetric matrix.
• Any square matrix can be expressed as the sum of a Symmetric and Skew symmetric matrix.
  ie; A = \(\frac{1}{2}\)(A + A^T) + \(\frac{1}{2}\)(A – A^T)
• If A and B are Symmetric matrices of the same order, AB is Symmetric if and only if AB = BA.
• If A and B are Symmetric matrices of the same order, (AB + BA) is Symmetric and (AB – BA) is Skew Symmetric.

V. Elementary Operation on Matrix
There are 6 operations on matrix, 3 for row and 3 for column.

1. The interchange of any two rows or two columns, symbolically denoted as R_i ↔ R_j or c_i ↔ c_j.
2. The multiplication of the elements of any row or column by a non-zero number, symbolically
   denoted as R_i ↔ kR_j or C_i ↔ kC_j.
3. The addition to the elements of any row or column, the corresponding elements of any other row or column multiplied by any non-zero number, symbolically denoted as R_i ↔ R_i + kR_j or C_i ↔ C_i + kC_j.

VI. Invertible Matrices
A square matrix B is said to be the inverse of a matrix A if AB = I = BA, then B is generally denoted
as A^-1.

1. Inverse of a square matrix, if it exists, is unique.
2. If A and B are invertible matrices of the same order, then (AB)^-1 = B^-1A^-1

Students can Download Chapter 6 Data Base Management System for Accounting Notes, Plus Two Accountancy Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus Two Accountancy Notes Chapter 6 Data Base Management System for Accounting

Database/ Data source – Introduction
A database is a collection of related data. It is organised in such a way that its contents can easily be accessed, managed and updated. In LibreOffice, database is also called data source. Database consists of interrelated data tables that are structured in a manner that ensures-data consistency and integrity. LibreOffice base, MS Access, Oracle, SQL server, etc. are the commonly used softwares for data base management.

Database Management System (DBMS)
DBMS is a collection of programs. It enables the users to create and maintain a data base. It is a general purpose software system that facilitates the process of defining, constructing and manipulating database for various applications.

Advantage of database/data source

1. All of the information is together
2. The information is portable
3. Information can be accessed at any time
4. Many users can access the same database at the same time.
5. Reduced data entry, storage and retrieval cost.

Disadvantages of database/Data source

1. Designing of database is a complex and time consuming process
2. Initial training is required for all the users
3. Installation cost is high

Basic concepts of LibreOffice Base

1. Entities: Anything in the real world is called entities. It may be person, place or things.
   Eg: Employee is an entity, Orange is an entry
2. Attributes: These.define the characteristics of an entity.
   Eg: Name, Age, Caste, Salary etc.
3. Identifiers: The unique attribute of an entity is called identifier. This is also called primary key.
   Eg: Admission number of a student, Aadhar Number of a person etc.
4. Relationships: These are the logical links between two entities or tables.

Components /Elements of LibreOffice Base

1. Fields: Individual pieces of data in a database are called fields.
2. Table: rows and columns to present fields in a database is called table. When creating a table, the characteristics of each field to be defined.
3. Forms: Forms are used to enter or modify data (fields) in to tables. Forms allow the user to display the data in a Table or Query.
4. Query: Query is a question. Queries are used to view, change and analyse data in different ways. It creates a new table from the existing tables based upon the question/ request asked to the data base.
5. Reports: It is used to create and present information based on queries in a easily readable format.

Planning (or designing) a database/ Data source
The first step in creating a database is to list down the various fields which are necessary for creating a database. The listed fields are used to create tables of the database. While entering fields into Tables, a primary key or an identifier is to be set for each table.

The primary key field cannot be left blank. The relationships of entities or tables can be created with the support of primary key. The relationships may be

• One -to-One
• One -to-Many
• Many-to-Many

The database created on the basis of relationships between different data tables is called relational database. The database design can be used to describe the structure of different parts of the overall data base. Avoiding the duplication of attributes/ fields is key criteria of database design.

Creating a new database
To Create a new database, select File → New → Database from the menubar, or click the arrow next to the New icon on the standard tool bar and select Database from the drop-down menu. Both methods open the Database wizard. On the first page of the Database wizard, Select create → a new databases → click Next.
The second page has two questions

1. Yes, register the data base for me
2. Open the database for editing.

Choose any one from the above and click Finish. In LibreOffice Base, the entire database is encompassed in a file with extension .odb. This file format is actually a container of all elements of the database, including Fields, Tables, Forms, Queries and Reports.

Creating database Tables
In DBMS, data is organised in Tables. A Table is a collection of data about a specific topic. Tables organise data into columns and rows. Each table is given a name. This is used to refer the table. The name depicts the content of the table. A database must have at least one table and may have several.

To work with Table, clicks the Tables icon in the Database list or Press Alt+A. The three tasks that we can perform on a table are in the Task list given below.

• Using the wizard to create a Table
• Creating a table by copying an existing table
• Creating tables in Design view.

1. Using the wizard to create a new Table:
Step 1: Open LiberOffice Base
Application → Office → LibreOfficeBase

Step 2: From the Data base wizard Screen, Create a database file or open an existing database file.
Select Database → Select Create a new database option and click on Finish button → then we get save dialogue box.

Step 3: Type appropriate file name. The default extension ‘.odb’ will be automatically added.

Step 4: Select location and click on Save

2. Using the wizard to open an Existing database:
Step 1: Open LibreOffice Base. From Database
wizard → Select open an existing database file option and click on Open button.

Step 2: Choose the file from the destination and click open.

3. Creating a table by Copying an existing table:
Step 1: Open LibreOffice Base
Application → Office → LibreOffice Base

Step 2: Click on the Tables icon in the database pane to see the existing tables
Select Database → Click on the Table icon → Right click on the Table from the Existing Tables.

Step 3: Choose Copy form the pop-up menu

Step4: Move the mouse pointer below the table, → right click → Select Paste. The copy Table dialogue opens.

Step 5: Change table name and click Next

Step 6:

Step 7: Click Create the new table is created

Step 8: Click the Save button at the top of the main database window.

4. Creating Tables in Design View:
Step 1: Click Tables from Data base Pane Database Pane → click Tables.

Step 2: Click Create Tables in design view in Tasks area. The design view of the new table will appear in the work area of the window.

Step 3: In design view, we can see three columns like Field Name, Field Type and Description. Create required field for the Table. Click Field Name cell → center Field names from top to bottom.

Step 4: Right click on the Field Name required to set as unique identifier for the tables, Select Primary Key option from the pop-up menu.

Step 5: In the Field Type, select appropriate field type from the combo box.

Step 6: In Description Field, we canenter appropriate description for each attributes.

Step 7: Save the table by providing table name.

5. Defining Relationships between Tables:
Relationships are used for connecting tables in database to get the advantage of data redundancy. Having completed the designs of all data tables, the next step is to establish relationships between different tables.
Step1: Click on the Tools menu and then Relationships

Step 2: Relation Design window opens and in the work area, a Add Tables dialogue box will appear.

Step 3: Select a Table and clik Add bottom to add it in the relationships.

Step 4: Add two tables in this manner after that click the close button.

Step 5: Create a relationship between two tables, Position the mouse pointer over desired field in table object, hold down the left mouse button, drag the pointer right to targeted field of the next table object and then release the mouse button.
This can also be done Insert → New Relation menu.

Creation of Forms in LibreOffice Base
Forms are used to input data into the database. In the language of database, a Form is a front end for data entry and editing. A Form is a window or screen that contain numerous fields or spaces to enter data. Each field holds a field label so that any user gets an idea of its contents.
The following two methods are used to create forms in LibreOffice Base

• Create Form in Design View
• Use wizard to create Form. The easy way to create Forms is use wizard to create Form.

1. Use Wizard to Create Form:
Step 1: Select Forms options from Database Pane

Step 2: Click on Use Wizard to Create Form Then. Form wizard window will appear.

Step3: Under the Table or queries, select Tables. The fields in the selected tables are listed in Available Fields list. Select the required field on by one and click on

Step 4 – After selecting the required field proceed by clicking Next.

Step 5 – Add sub Form fields. This step is similar to step 3

Step 6 – Get joined Fields.
This step is for tables and queries for which no relationships has been defined. The wizard skip this step. Because we have already defined the relationship.

Step 7: Arrange controls: A control in a Form consist of two parts: label and field. This step in creating the Form determines where a controls label and field are placed relative each other. Four choices are available.

Step 8: Set data entry: It is better to accept the default settings. Click Next.

Step 9: Apply styles: The background colour, field boarder etc. can be selected from this options.

Step 10: Set the name of the form: we can give the name of the Form we are creating. The name must be unique and must have a relation with the data to be stored → click Finish. The Form opens in Edit mode.

Entering data in a form
The text box can be used to add data in the Form. Click on the text Box Icon, and click on the work area. The cursor will be positioned on the Top left of the work area. Then the matter is to be added. The text entered can be formatted. Images can also be inserted in the Form by selecting Image Insert Icon.

Creation of Query in LibreOffice Base
Queries are used to get specific information from the database. Queries are also used to manipulate the database content. Structured Query Language (SQL) is the most widely-used query language. LibreOffice Base also uses SQL command for querying its database. The query operations can be done in two different ways.

• Using the wizard to create a query
• Using the design view

1. Using the wizard to create a query:
Step 1: Selection of Fields
The first step in Query wizard is field selection. All the tables included in the data base can be seen in the Table list select the appropriate Table. All the fields of the selected table can be seen in the Available Fields list.

The user can select the fields needed from the list using the tools arranged right to Available fields list. The selected fields can be seen in Fields in the Query list. The order of the selected fields can change using the tools (∧ and ∨) right to Fields in the query list. Then, press Next button or Finish button.

Step 2: Select the sorting order: In this step, the field name to sort the query result can be selected. (Skip this step, if no sorting is needed).

Step 3: Select the search conditions: This step specifies the search conditions to filter the query. (Skip the step, if no filtering is needed).

Step 4: Details of summary: This page specifies whetherto display all records of the query, or only the results of aggregate functions. This page is only displayed when there are numerical fields in the query that allow the use of aggregate functions.

Step 5: Grouping conditions: Specfies wheter to group the query. The data source must support the SQL statement “order by clause” to enable this page of the wizard.

Step 6: Assign aliases if desired: – Thisjsage helps to assign aliases to field name. Aliases are optional, and can provide more user- friendly names, which are displayed in place of field names.

Step 7: Overview: This wizard page gives an overview of the query made. It helps to enter a name of the query, and specifies whether to display or to modify the query afterthe wizard is finished.

Step 8: Press Finish button after the completion of Query wizard entry. The Query will be saved. The user can run this query at any time.

Step 9: Run the saved Query: Select Queries option from the left panel of the LibreOffice Base window. The saved query can be seen in the right side. Double click on the query name to run the query.

2. To create query in design view:

• Step 1: Use the option Create Query in Design view from Base window to create query in design view.
• Step 2: Use Add Table or Query dialogue to include table(s) to query design.
• Step 3: Include the fields and formula in the top row and give aliases in the second now, if needed.
• Step 4: Press Run Query button to execute the query.

Creation or Reports in LibreOffice Base
Information from a database can be generated through the Reports in LibreOffice Base. The reports can be printed and formatted as perthe requirements of user. The reports can be edited, printed and exported to PDF format.
The reports can be created by the following two ways.

• Create Report in Design view
• Use wizard to ere ate Report

1. Use wizard to create Report in LibreOffice Base:

• Step 1: Click the icon Reports in Database pane
• Step 2: Click on Use wizard to create Report option in Task area.
• Step 3: Select table or query from the drop down option for which reports need to be created.
• Step 4: Select the required fields
• Step 5: Enter title for the report in the field Title of the report and click on Finish button.
• Step 6: The report generated is in the read only mode. It can be edited by clicking on Edit Document option.

In short, When the Report wizard is opened, the Report Builder is also opened. As we make our selections in the wizard these appear in layout in the Report Builder. After finishing the selections, save the report, name it and then close it.

Accessing other Data Sources
LibreOffice Base allows other data sources to be accessed and linked into LibreOffice documents. To acess a data source which is not a .odb file.

• Step 1: File → New → Database opens the Data base wizard window.
• Step 2: Select Connect to exisiting data base. Click the arrow next to Data base type field and select the Database type from drop down list. Click Next.
• Step 3: Click Browse and select the database click Next.
• Step 4: Accept the default settings: Register the data base for me, and open the database for editing. Click Finish. Name and save the database in the location of our choice.

1. Accessing a spreadsheet as a data source:

• Step 1: Choose File → New → Data base.
• Step 2: Select Connect to an existing database. Select Spread sheet as a database type.
• Step 3: Click Browse to locate the spreadsheet we want to access. If spreadsheet is password protected, Check the password required box, click Next.
• Step 4: If the spreadsheet requires a users name, enter it. If a password is also required, check its box. Click Next → save the file.

2. Registering *.odb databases:
Databases created by LibreOffice base are in the *.odb format. Other programs can also produce database in this format. Registering a*.odb data base is simple.

• Step 1: Select Tools → Options → Libre Office Base → Database
• Step 2: Under Registered data Bases, Click New.
• Step 3: Browse to where the database is located.
• Step 4: Make sure the registered name is correct .Odb
• Step 5: Click OK.

Using data sources in LibreOffice
Any data source registered in spreadsheet or text document can use in other LiberOffice components including writer and calc.

1. Viewing data sources:
Open a document in writer or calc. To view the data sources available, Press F4 or select View → Data sources from the pull down menu. This brings up a list of registered databases. To view each data base, click on the arrow to the left of the database’s name.

2. Editing Data sources:
Some data sources can be edited in the Data view window. A record can be edited, added or deleted. Editing the data requires only a click in the cell whose data should be changed. To delete the record, right click on the gray box to the left of row to highlight the entire row, and select Delete row to . remove the selected row.

3. Launching Base to work on data sources:
We can launch LibreOffice Base at any time from the Data source window. Just right click on a database, or its tables or Queries icons and select Edit Database File. In Base, we can edit, add, and delete tables, queries, forms and reports.

4. Using Datasources in writer and Calc.:
Data can be placed into writer and Calc documents from the tables in the data source window. In writer, values from individual fields can be inserted. Or a complete table can be created in the writer document. One common way to use a data source is to perform a mail merge.

Students can Download Chapter 7 The p Block Elements Notes, Plus Two Chemistry Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus Two Chemistry Notes Chapter 7 The p Block Elements

The p-block – Elements of group 13 to 18 of the periodic table. The outer electronic configuration of a p-block element is ns²np^1-6.

Anomalous behaviour of the first element of a group: This is due to

1. Small in size
2. High electronegativity,
3. High ionisation enthalpy and
4. Non-availability of d – orbitals.

Diagonal Relationship:
In some cases, the first element of a group resembles diagonally with the element of the next group and of the next period.

Group 15 – Elements – Nitrogen Family:
Elements are – N, P, As, Sb, Bi
N₂ comprises 78% by volume of the atmosphere. N and P are essential constituents of animals and plants. N – Present in proteins, P – Present in bones.

Characteristics:
1. Atomic radii increases with increase in Atomic Number.

2. Ionisation Enthalpy decreases down the group due to gradual increase in atomic size. Because of the extra stable half-filled p orbitals electronic configuration and smaller size, the ionisation enthalpy is less than that of group 14 elements in the corresponding periods.

3. Electronegativity decreases down the group.

Physical Properties:
All are polyatomic, metallic character increases from N to Bi, density increases from N to Bi, M.P. and B.P. increases down the group, except N all other elements show allotropy.

Chemical Properties:
Oxidisation states and trends in chemical reactivity:
The common oxidation states of 15 group elements are (-3), (+3) and (+5). The stability of +5 oxidisation state decreases and that of +3 state increases down the group due to inert pair effect. Nitrogen exhibits +1, +2, +4 oxidation states also when it react with O₂.

The maximum covalence of N restricted to 4 since only 4 orbitals (one S and three P) are available for bonding.

Anomalous Properties of Nitrogen:
It is due to its small size, high electronegativity, high ionisation enthalpy and non-availability of ‘d’ orbitals. Nitrogen has unique ability to form pπ – pπ multiple bond. It cannot form dπ – pπ bond. P and A scan form dπ – dπ bond.

(i) Reactivity towards hydrogen:
EH₃ hydrides, the central atom is sp³ hybridised, molecules assume trigonal pyramidal geometry with a lone pair on the central atom. Stability-decreases from NH₃ to BiH₃.

This is because, down the group the E-H bond dissociation enthalpy decreases due to increase in size of the central atom. Consequently, reducing character increases from NH₃ to BiH₃. The basicity decreases in the order NH₃ > PH₃ > AsH₃ > SbH₃> BiH₃.

As the electro negativity of the central atom decreases on moving down the group, the bond pair-bond pair repulsion decreases. Hence the bond angle decreases in the order NH₃ > PH₃ > AsH₃.

(ii) Reactivity towards oxygen:
They form E₂O₃ & E₂O₅ type oxides. The oxide in the higher oxidisation state of the element is more acidic than that in lower oxidation state.

(iii) Reactivity towards halogens:
They form EX₃ and EX₅ type halides. Nitrogen does not form pentahalide due to non-availability of d-orbital.

(iv) Reactivity towards Metals:
They react with some metals exhibiting – 3 oxidation state, e.g. Calcium nitrate (Ca₃N₂), Calcium phosphide (Ca₃P₂), Sodium arsenide (Na₃As₂).

Dinitrogen (N₂):
It is produced commercially by the liquefaction and fractional distillation of air.
In laboratory, N₂ is prepared by

NH₄Cl(aq) + NaNO₂(aq) → N₂(g) + 2 H₂O(l)+ NaCl(aq)

Properties:
Colourless, odourless, non-toxic gas; inert at room temperature because of high bond enthalpy of N ≡ N.

Uses:
Manufacture of NH₃, liquid N₂ is used as refrigerant to preserve biological materials, food items and in cryosurgery.

Ammonia:
Laboratory preparation:
2NH₄Cl + Ca(OH)₂ → 2NH₃ + 2H₂O + CaCl₂
(NH₄)₂SO₄ + 2NaOH → 2NH₃ + 2H₂O + Na₂SO₄

Industrial (large scale) preparation by Haber’s process:
N₂(g) + 3H(g) ⇌ NH₃(g); Δ_fH^Ⓗ = -46.1 kJ/mol^-1 Catalyst used earlier- spongy iron with molybdenum promoter. Catalyst used now – iron oxide with small amounts of K₂O and Al₂O₃.

High pressure and low temperature will favour the formation of NH₃ as the forward reaction is exothermic and is accompanied by decrease in number of moles (Le Chatelier’s principle). Hence, a pressure of 200 × 10⁵ Pa (about 200 atm) and a temperature of ~ 700 K are employed to increase the yield of NH₃.

Properties:
Colourless, pungent smelling gas, trigonal pyramidal geometry, highly soluble in water.
NH₃(g) + H₂O(l) \(\rightleftharpoons\) NH⁺₄(aq) + OH^–(aq)
Lewis base – due to the presence of a lone pair of electrons on N. It can form complex compounds with metal ions. This finds application in the detection of
Cu²⁺ and Ag⁺.

Uses:
To produce various nitrogeneous fertilizers, manufacture of inorganic nitrogen compounds (e.g. HNO₃), liquid NH₃ is used as a refrigerant.

Oxides of Nitrogen:

1. Dinitrogen oxide (N₂O) or laughing gas – Oxdation state (+1) – Colourless gas, neutral.
2. Nitrogen monoxide(NO) – Oxdation state (+2) colourless gas, neutral.
3. Dinitrogen Trioxide(N₂O₃) – Oxdation state (+3), blue solid, acidic in nature.
4. Nitrogen dioxide(NO₂) – Oxdation state (+4) brown gas, acidic. It contains odd number of valence electrons. On dimerisation, it is converted to stable N₂O₄ molecule with even number of electrons.
5. Dinitrogen tetroxide(N₂O₄) – Dimer of NO₂ – Oxdation state (+4), colourless solid/liquid, acidic.
6. Dinitrogen pentoxide (N₂O₅) – Oxdation state (+5), colourless solid, acidic.

Nitric Acid:
It is the most important oxoacid of N.
Laboratory preparation:
KNO₃/NaNO₃ + H₂SO₄(conc.) → KHSO₄/NaHSO₄ + HNO₃
Industrial preparation – Ostwald’s process:
(1) NH₃ oxidised to NO by air.

(2) NO is converted to NO₂
2NO(g) + O₂(g) ⇄ 2NO₂(g)

(3) NO₂ dissolved in water to give HNO₃
3NO₂(g) + H₂O(l) → 2HNO₃ (aq) + NO(g)

Properties:
Colourless liquid, strong acid in aqueous solution. Concentrated HNO₃ is a strong oxidising agent and attacks most metals except noble metals like Au and Pt. The products of oxidation depend upon the concentration of the acid, temperature and the nature of the material undergoing oxidation, e.g.

• 3Cu + 8HNO₃(dilute) → 3Cu(NO₃)₂ + 2NO + 4H₂O
• Cu + 4HNO₃(conc.) → CuCu(NO₃)₂ + 2NO₂ + 2H₂O
• 4Zn + 10HNO₃(dilute) → 4Zn(NO₃)₂ + 5H₂O + N₂O
• Zn + 4HNO₃(conc.) → Zn(NO₃)₂ + 2H₂O + 2N₂O

Some metals (e.g., Cr, Al) do not dissolve in concentrated nitric acid because of the formation of a passive film of oxide on the surface.

Structure:
In the gaseous state, HNO₃ exists as a planar molecule.

Uses:
Manufacture ammonium nitrate (fertilizer), preparation of explosives, preparation of nitroglycerine, pickling of stainless steel, etching of metals, oxidiser in rocket fuels.

Phosphorus:
Allotropic forms – White P, red P and black P

White Phosphorus:
Transient white waxy solid, poisonous, insoluble in water, soluble in CS₂, glows in dark (chemiluminescence), kept underwater, less stable and therefore more reactive than other solid phases under normal conditions because of angular strain in discrete tetrahedral P₄ molecules (angle 60°), readily catches fire in air and gives dense while fumes of P₄O₁₀.
P₄ + 5O₂ → P₄O₁₀

Red Phosphorus:
Obtained by heating white P at 573 K in an inert atm for several days, possesses iron grey lustre, odourless, non-poisonous, less reactive than white P, does not glow in dark, polymeric consisting of chains of P₄ tetrahedra.

Black Phosphorus:
Obtained when red P is heated under high pressure, two forms α – black phosphorus (formed when red P is heated in a sealed tube at 803 K) and β – black phosphorus (prepared by heating white P at 473 K under high pressure).

Phosphine (PH₃):
Prepared by the reaction of calcium phosphide with water or dilute HCl.
Ca₃P₂ + 6H₂O → 3Ca(OH)₂ + 2PH₃
Ca₃P₂ + 6HCl → 3CaCl₂ + 2PH₃

Laboratory preparation:
By heating white P with con centrated NaOH solution in an inert atmosphere of CO₂.
P₄ + 3NaOH + 3H₂O → PH₃ + 3NaH₂PO₂

Properties:
Colourless gas with a rotten fishy smell, highly poisonous, weakly basic, the structure is similar to NH₃ and gives phosphonium compounds with
acids. PH₃ + HBr → PH₄Br
Uses: in Holme’s signals, in smoke screens.

Phosphorus Halides:
It forms two types of halids PX₃ and PX₅ (X = F, Cl, Br)

Phosphorus Trichloride (PCl₃):
Obtained by passing dry Cl₂ over heated white P.
P₄ + 6Cl₂ → 4PCl₃

Or, by the action of thionyl chloride on white P,
P₄ + 8SOCl₂ → 4PCl₃ + 4SO₂ + 2S₂Cl₂

Properties
Colourless oily liquid, hydrolyses in the presence of moisture giving fumes of HCl.
P₄ + 3H₂O → H₃PO₃ + 3HCl
It has pyrimidal shape and P is sp3 hybridised.

Phosphorus Pentachloride (PCl₅):
Preparation:
White P₄ + 10Cl_2(dry) → 4PCl₅

Properties:
yellowish white powder. In moist air it hydrolysed giving POCl₃ and finally gets converted to phosphoric acid (H₃PO₄)
PCl₅ + H₂O → POCl₃ + 2HCl
POCl₃ + 3 H₂O → H₃PO₄ + 3 HCl
In gaseous and liquid phases, the shape of the molecule is trigonal bipyramidal. There are two types of P-Cl bonds, equatorial bond and axial bond. Axial bonds are longer than equitorial bonds due to more repulsion. In solid state it exits as ionic solid, [PCl₄]⁺[PCl₆]^–.

Oxoacids of Phosphorus:

• Hypophosphorous/Phosphinic acid(H₃PO₂) – Monobasic
• Orthophosphorous/Phosphonic acid(H₃PO₃) – Dibasic
• Pyrophosphorous acid(H₄P₂O₅) – Dibasic
• Hypophosphoric acid(H₄P₂O₆) – Tetrabasic
• Orthophosphoric acid(H₃PO₄) – Tribasic
• Pyrophosphoric acid(H₄P₂O₇) – Tetrabasic
• Metaphosphoric acid(HPO₃)_n – Tribasic

The p-H bonds are not ionisable and have no role in basicity. Only those H atoms in P-OH form are ionisable and cause basicity.

These acids in +3 oxidation state of P tend to disproportionate to higher and lower oxidation states, e.g. Orthophosphorous acid on heating disproportionates to give orthophosphoric acid (P in +5 state) and phosphine

The acids with P-H bond .have strong reducing property, e.g. H₃PO₂. It reduces AgNO₃ to Ag.

Structure of Oxoacids:

Group 16 Elements (Chalcogens):
O, S, Se, Te and Po.

1. Occurrence:
O₂ – Most abundant element on earth crust (46.6%), dry air contains 21% by volume. S – Present as sulphates, sulphides (e.g. CaSO₄, PbS, ZnS). Se &Te-in metal selenides and tellurides, Po-radio active, formed by the decay of thorium and uranium minerals.

2. 6 General electronic configuration-ns²np⁴. In group:
Atomic and ionic radii increases, ionisation enthalpy, electron gain enthalpy and electronegativity decreases – O has the highest electronegativity next to F.

3. Physical Properties:
O is a diatomic gas, non metal. S-solid, non-metal. Se and Te are metalloids. Po-radioactive metal.

4. Chemical Properties:
Oxidation states and trends in chemical activity – exhibits variable oxidation states, stability of -2 oxidation state decreases down the group. O-shows +2 in OF₂, -1 in peroxides and – 2 in other compounds. Other elements show +2, +4, +6 states.

5. Anomolous Behaviour of Oxygen:
It is due to small size high electronegativity, non availability of d-orbital and high polarising power.

(i) Reactivity with Hydrogen:
group 16 elements form H₂E type hydrids (E = O, S, Se, Te, Po). Their acidic character increases from H₂O to H₂Te due to decrease in H-E bond dissociation enthalpy. All hydride except H₂O posses reducing property. Reducing nature increases from H₂S to H₂Te.

Due to small size and high electro naegativity of oxygen, H₂O molecules are highly associated through hydrogen bonding resulting in its liquid state and high boiling point.

While, due to large size and low electronegativity of S association through hydrogen bonding is hot possible in H₂S. Hence it exists as a gas and has low boiling point than H₂O.

(ii) Reactivity with Oxygen:
They form EO₂ & EO₃ type oxides. Ozone, O₃ and SO₂ are gases. Both type of oxides are acidic in nature.

(iii) Reactivity Towards the Halogens:
They form EX₂, EX₄ and EX₆ type halides. The stability of halides decrease in the order F^– > Cl^– > Br > l^–

Dioxygen (O₂):
Preparation:
(i) Heating KClO₃, KMnO₄, KNO₃ etc.

(ii) Thermal decomposition of metal oxides.
2Ag₂O → 4Ag + O₂
2PbO₂ H → 2PbO + O₂

(iii) Decomposition of H202
2H₂O₂ → 2H₂O + O₂.

Large scale preparation:
Electrolysis of water, O₂ liberated at anode.

Properties:
Colourless, odourless gas; paramagnetic, directly reacts with nearly all metals except Au and Pt.

Simple Oxides:
Binary compound of O with another element, e.g. MgO, Al₂O₃. Basic oxide – oxide that combine with water give a base. e.g. MgO. Acidic oxide – oxide that combine with water to give acid, e.g. SO₂, CO₂.
SO₂ + H₂O → H₂SO₃
In general, metallic oxides are basic and non-metallic oxides are acidic.

Ozone (O₃):
Allotropic form of O, too reactive, prepared by passing a slow dry stream of O₂ through a silent electrical discharge.
3O₂ → 2O₃
ΔH = +142 kJ mol^-1

Properties:
Pure O₃ is a pale blue gas, dark blue liquid and violet-black solid, thermodynamically unstable compared to O₂.

Oxidising property:
Due to the ease with which it liberates atoms of nascent oxygen 03 acts as a powerful oxidising agent.
O₃ → O₂ + [O]
e.g. It oxidises lead sulphide to lead sulphate.
PbS(s) + 4O₃(g) → PbSO₄(s) + 4O₂(g)

Estimation of O₃:
When O₃ reacts with excess of Kl solution buffered with a borate buffer (pH 9.2), l₂ is liberated which can be titrated against a standard solution of sodium thiosulphate.
2l^–(aq) + H₂O(l) + O₃(g) → 2OH^–(aq) + l₂(s) + O₂(g)

Uses:
As a germicide, disinfectant and for sterilising water; for bleaching oils, ivory, starch etc. as oxidising agent in the manufacture of KMnO₄.

Sulphur-Allotropic Forms:
Rhombic Sulphur (α – Sulphur):
yellow, insoluble in water, dissolve to some extent in benzene and alcohol, readily soluble in CS₂.

Monoclinic Sulphur (β – Sulphur):
Soluble in CS₂, needle shaped crystals.

Structure:
They exists as S₈ molecules, the S₈ ring is puckered and has a crown shape. The cylco-S₆ ring adopts a chair form.

Sulphur Dioxide (SO₂):
Preparation:
1. Burning of S in air
S(s) + O₂(g) → SO₂(g)

2. Treating sulphite with diluted H₂SO₄.
SO₃^2- + 2H⁺ → H₂O + SO₂

Properties:
Colourless gas with pungent smell, highly soluble water, when passed through water forms sulphurous acid.
SO₂(g) + H₂O(l) → H₂SO₃(aq)

React with NaOH:
2NaOH + SO₂ → Na₂SO₃ + H₂O

Other reactions:
3SO₂ + Cl₂ → SO₂Cl₂

Users:
In pertroleum refining and sugar industry, in bleaching wool and silk, in manufacturing H₂SO₄.

Oxoacids of Sulphur:
Sulphur forms a number of oxoacids such as H₂SO₃, H₂SO₄, H₂S₂O₃, H₂S₂O₇

Manufacture of Sulphuric Acid:
Sulphuricacid is known as king of chemicals. It is manufactured by Contact Process.

Steps Involved:
(i) Burning of S or Sulphide ores in air to form SO₂

(ii) Conversion of SO₂ to SO₃ by the reaction with O₂ in presence of V₂O₅ catalyst.

ΔH = -196.6 KJ mol^-1
Low temperature (720 K) and high pressure (2 bar) are the favourable conditions for maximum yield.

(iii) Absorption of SO₃ in H₂SO₄ to give oleum (H₂S₂O₇)
SO₃ + H₂SO₄ → H₂S₂O₈
Dilution of oleum with water gives H₂SO₄ of desired concentration. H₂S₂O₇ + H₂O → 2 H₂SO₄

Properties:
Colourless, oily liquid, dissolves in water with the evolution of large quantity of heat, dibasic acid, in aqueous solution, it ionises in two steps:
H₂SO₄(aq) + H₂O(l) → H₃O⁺(aq) + HSO₄^– (aq)
HSO₄^–(aq) + H₂O(l) → H₃O⁺(aq) + SO₄^2-(aq)
Concentrated H₂SO₄ is a strong dehydrating agent.

Uses:
Manufacture of fertilisers; petroleum refining; manufacture of pigments, paints, dyestuff; detergent industry; storage batteries; laboratory reagent

Group 17 Elements (Halogens): F, Cl, Br, I and At (radio active), highly reactive non-metallic elements.

1-6 Occurrence:
F-in fluorides (CaF₂, Na₃AIF₆). Sea water contains chlorides, bromides and iodides of Na & K, electronic configuration – ns²np⁵, in a group from top to bottom atomic and ionic radii increases, ionisation enthalpy decreases.

Electron gain enthalpy – halogen have maximum negative electron gain enethalpy. Cl has highest electron gain enthalpy. Electro negativity decreases down the group. F is the most electronegative element in the periodic table.

Physical Properties:
F₂, Cl₂ – gases, Br₂ – liquid and l₂ – solid. F₂ and Cl₂ react with water Br₂ and l₂ sparingly soluble in water.

Oxidation States and Trends in Chemical Reactivity:
All the halogens exhibit-1 oxdn. state. But, Cl, Br and I exhibit +1, +3, +5 and +7 also. They react with metals and non-metals to form halides. The reactivity of the halogens decreases down the group.

Anomalous Behaviour of Fluorine:
It is due to smaller in size, high electronegativity, low F-F bond dissociation enthalpy and non-availability of d-orbitals, due to which it cannot expand its octet. It exhibits only-1 oxidation state.

(i) Reactivity Towards Hydrogen:
All form hydrogen halides (HX) which dissolve in water to form hydrohalic acids. The acidic strength of acids:
HF < HCl < HBr < Hl .The stability of halides decreases down the group due to decrease in (H-X) dissociation enthalpy in the order: H-F > H-Cl > H-Br > H-l.

(ii) Reactivity Towards Oxygen:
They form many oxides but most of them are unstable. Fluorine form OF₂ and O₂F₂. Chlorine form oxides Cl₂O, ClO₂, Cl₂O₆ and Cl₂O₇, which are highly reactive oxidising agents, ClO₂ is used as a bleaching agent for paper pulp, textiles.

(iii) Reactivity Towards Metals:
Metal halides are formed,
e.g. Mg(s) + Br₂(l) → MgBr₂(s)

(iv) Reactivity of Halogens Towards Other Halogens:
Halogens combine amongst themselves to form a number of compounds known as interhalogens. Five types: XX’, XX3, XX’5, XX’7 where X is a halogen of larger size and X’ of smaller size.

Chlorine:
Preparation:
(i) By heating manganese dioxide with concentrated HCl.
MnO₂ + 4HCl → MnCl₂ + 2H₂O + Cl₂

(ii) By the action of HCl on KMnO₄.
2KMnO₄ + 16HCl → 2KCl + 2MnCl₂ + 8H₂O + 5Cl₂

Manufacture:
(i) Deacon’s Process – By oxidation of HCl gas by atm oxygen in the presence of CuCl₂ at 723K.

(ii) Electrolytic process
 (liberated at anode)

Properties:
Greenish yellow gas with pungent and suffocating odour, reacts with metal, and non metals

With excess NH₃, Cl₂ gives N₂ and NH₄Cl whereas with excess Cl₂, NH₃ gives NCl₃ (explosive) and HCl.

With cold and dilute alkalies chlorine produces a mixture of chloride and hypochlorite but with hot and concentrated alkalies it gives chloride and chlorate.

With dry slaked lime, it gives bleaching powder.
2Ca(OH)₂ + 2Cl₂ → Ca(OCl)₂ + CaCl₂ + 2H₂OCl₂ is a powerful bleaching agent.
Cl₂ + H₂O → 2HCl + [O]
Coloured substance + [0] → colourless substance

Uses:
For bleaching wood pulp, cotton and textiles; for the preparation of insectiside, pesticides and other organic solvents, e.g. CHCl₃, DDT, BHC etc.

Hydrogen Chloride (HCl):
Preparation:

HCl gas is dried by passing through a cone. H₂SO₄.
Properties :
Colourless and pungent smelling gas, soluble in water and ionises as follows:
HCl + H₂O → H₃O⁺ + Cl^–
It reacts with NH₃ to give white fumes of NH₄Cl.
NH₃ + HCl → NH₄Cl
It decomposes salt of weaker acids.
Na₂CO₃ + 2HCl → 2NaCl + H₂O + CO₂
NaHCO₃ + HCl → NaCl + H₂O + CO₂

Uses: manufacture of Cl₂, NH₄Cl and glucose; for extracting glue.

Oxoacids of Halogen:
Due to high electronegativity and smaller in size fluorine forms only one oxoacid, HOF known as fluoric acid or hypofluorous acid.

Some oxoacids of Chlorine:

• Hypochlorous acid: HOCl (Cl in +1 state)
• Chlorous acid: HClO₂ (Cl in +3 state)
• Chloricacid: HClO₃ (Cl in +5 state)
• Perchloricacid: HClO₄(Cl in +7 state).

Interhalogen Compounds:
Two different halogens react to form inter halogen compounds, e.g. ClF, ClF₃, BrF₅, IF₇

Preparation:
By the direct combination of halogens.

Properties:
Covalent molecules, diamagnetic, volatile solids or liquids at 25°C except ClF which is a gas. They are more reactive than halogens because X-X bond is weaker than X-X bond. Due to electronegativity difference the X – X bond is polarised, hence it is reactive.

Their stability increases as the size difference of the halogens increases due to increase in the polarity of the bond. e.g. IF₃ is more stable than ClF₃.

Group 18 Elements (Noble Gases):
He, Ne, Ar, Kr, Xe and Rn (radio active). Except He all other noble gas have 8 electrons in the valence shell. Due stable electronic configuration all these are gases and chemically unreactive, (exeption – Kr, Xe, Rn)

Occurrence:
All except Rn occur in the atmosphere. The main source of He-natural gas. Rn- obtained as a decay of product of Radium.

Electronic Configuration-ns²np⁶ (except He-1s² ), ionisation enthalpy-high due to stable electronic configuration-it decreases down the group, atomic radii-increases down the group, electron gain enthalpy-almost zero since no tendency to accept an electron.

Physical Properties:
Monoatomic, colourless, odourless and tasteless gases, sparingly soluble in water, very low melting and boiling points because the only type of interatomic interaction in these elements is weak dispersion forces.

Chemical Properties:
Least reactive due to stable electronic configuration, high ionisation enthalpy and more positive electron gain enthalpy.

N. Bartlett prepared Xe⁺PtF₆ by mixing PtF₆ and Xe.

(a) Xenon – Fluorine Compounds:
Xe forms three binary fluorides XeF₂, XeF₄ and XeF₆ by the direct reaction of Xe with F₂.

XeF₄^– also prepared by reaction with O₂F₂ and XeF₄. XeF₄ + O₂F₂ → XeF₆ + O₂

Structure:
(a) XeF₂ – sp³d hybridisation -linear
XeF₄ – sp³d² hybridisation – square planar
XeF₆ – sp³d³ hybridisation – distorted octahedral

(b) Xenon-Oxygen Compounds:
XeO₃: Prepared by hydrolysis of XeF₄ and XeF₆.
6XeF₄ + 12H₂O → 4Xe + 2XeO₃ + 24HF + 3O₂
XeF₆ + 3H₂O → XeO₃ + 6HF.
XeOF_4^–prepared by partial hydrolysis of XeF₆.
XeF₆ + H₂O → XeOF₄ + 2HCl

Structure:
XeO₃ – sp³ hybridisation – Pyramidal
XeOF₃ – sp³d² hybridisation – Square pyramidal

Uses of Noble Gases:
1. He – for filling airships, aeroplane tyres, in gas-cooled nuclear reactors, for providing an inert atmosphere in the welding of metals and alloys.

2. Ne – for filling discharge tubes and fluorescent bulb for advertisement purpose, in botanical gardens and greenhouses.

3. Ar – to provide inert atmosphere in high-temperature metallurgical processes, for filling electric bulbs, for handling air-sensitive substances in laboratory.

4. Xe and Kr – in light bulbs designed for special purposes.