Biripali

  Electric potential :-         C url of electrical field is zero therefore, electric field is conservative field. Scalar potential is defined only for conservative field.        In the following we first show that curl of electric field is zero . We know field of a point charge at the origin.      If we take the integral along a closed path Then, . Apply Stoke theorm   Here,  This result can be generalised for any charge distribution using the principal of superposition. The general result is 

  LATTICE VIBRATION:-      E very atom has a tendency to vibrate about their mean position at temperature above zero Kelvin. The mean position is referred as the Bravais lattice site . These vibrations occur due to interatomic interactions. As the atoms in the solids are present at lattice sites , so these vibrations are called lattice vibrations. Fig.1            Lattice vibration are the results of absorption of heat energy. A lattice is an array of atoms connected with each other by elastic springs or strings .      Here all the atoms present at lattice sites are coupled and the motion of one single atom is shared by the neighbouring atoms. Thus the crystal vibrates on a whole . The dynamic external forces which are responsible for the vibrations obey Hooke's law. It is assumed that the amplitude of the vibrations are small as compared to the interatomic spacing. Harmonic approximation is valid for lattice vibrations. T...

  HYSTERESIS (B-H CURVE) :           C onsider a ferromagnetic substance (iron bar) is placed in a magnetizing field. As magnetizing field H is slowly increased, the intensity of magnetization also increases. The graphical representation of the extent of magnetization at different value of H. To start with H = 0 and magnetization B is also zero. As H increases B also increases along the curve OA. State of saturation is reached at A  and further increases of H will not increase B.           Now if we decrease H , the demagnetization of the sample does not take place along the curve AO. Thus  as H is decreased and becomes zero then it is seen that B does not become zero but has the value OG called retentivity. Hence demagnetisation lags behind the magnetizing field H. This phenomena in which B lags behind the magnetizing field H is called Hysteresis. The residual magnetism left behind in the magnetic substance when magn...

Diffraction of x-rays by crystals:      X -rays can be diffracted by crystals in the same way as the visible light is diffracted by a diffraction grating. So crystal can act like diffraction gratings. The idea that crystals can diffraction x-rays was given by  Von laue .    X-rays form part of the electromagnetic spectrum which were discovered by Roentgen. From the optical properties of x-rays , Sommerfeld estimated that the wavelength of x-rays is about 10^-10m. Crystalographers has estimated from a knowledge of density and molecular mass that spacings between two lattice points in a crystal is also about 10^-10m. From these two physical facts it occurred to max Von laue that crystals serve as diffraction gratings for x-rays and show the phenomena of diffraction. He took the help of his colleagues Friedrich and knipping. X-rays were used for demonstration of diffraction in crystal due to the fact that the wavelength of x-rays is comparable to the interatom...

  RECIPROCAL LATTICE:-   M any properties of crystalline substance are different in different directions. W.H.Miller explain the concept of miller indices to represent the planes and directions of a crystal. In real practice there are many set of planes with different orientations and spacings and it becomes difficult to visualise the slope of the planes. Since all parallel planes have a common normal and simillar indices , so the miller indices of a plane can not be uniquely defined. Therefore to understand many crystallographic problem we consider the normal to be set of planes rather than the planes themselves. The orientation of plane is understood by the direction of normal. DEFINITION OF RECIPROCAL LATTICE:-       T he reciprocal lattice in Fourier space is an infinite periodic three dimensional array of points whose spacings are inversely proportional to the distance between planes in the direct lattice.     The need for devising the concept of ...

                            Solids:-    Sol ids : The solids are the forms of matter in which atoms ands molecules are strongly bound and maintain definite volume and sharp unless changes by applying external forces. Solid state physics: - The solid state physics is the study of the physical properties of the atomic/molecular matter in the solids state. These physical properties include crystal structure, bonding,thermal, electric and magnetic properties. Classification of solids:         Solids are classified into two categories; (1) crystalline solids (2) Amorphous solids. (1) crystalline solid :-        The crystalline solids are defined as an ordered periodic arrangements of atoms, molecules or ions . Properties of crystalline solids:- • The internal arrangements of atoms,ions or molecules of crystalline solids is in a definite order. • The crystalline solids have ...

Post ulates of kinetics theory :-        Suppose a container with volume v contain a very large numbers N of identical molecules,each with mass m. Then, the kinetics theory postulates the following- (1) The molecules behave a point particles that are small compared to the size of the container and to the average distance between molecules. (2) The molecules are in constant motion. Each molecules collides occasionally with a wall of the container. These collisions are perfectly elastic. (3) There is no force of attraction among the gas molecules and between the gas molecules and walls of the container. (4) The container walls are right and infinitely massive and do not move. (5) The molecules obey Newton's law of motion. (6) The time of collision is much less than the averaged time between two successive collision. Meaning of elastic collisions:- If a molecule with velocity u strikes a wall align along y-axis, then the collision is elastic if • velocity componen...

Coulomb's Law : The electrostatic force of interaction between two static point electric charge is directly proportional to the product of the charge, inversely proportional to the square of the distance between them and acts along the straight line joining the two charges. If two points charge q1 and q2 separately by a distance r. Let F be the electrostatic force between these two charge. According to Coulombs law.

I) In term of energy:-       Kinetic energy of a potential of mass m moving with velocity v is given by Where p is momentum of particles Therefore, We knowing that de- Broglie wavelength                  λ= h/p Therefore,   ........................(1) II) In term of temperature:-  From kinetic energy of gases, the average kinetic energy of a material particles at temperature T is given by Where k is Boltzmann constant. The value of k= 1.38 x 10^-23 J/k Putting this value in eq (1), we get Therefore, ...................(2)

Electric charge: Charge is the property associated with matter due to which it produces and experience electrical and magnetic effect.The excess or deficiency electrons in a body gives the concept of charge. Types of charge: 1. positive charge: It is deficiency of electrons as compared to protons. 2. Negative charge: It is excess of electrons as compared to proton. S.I. Unit of charge is Coulomb Dimensions: [A T] 1C = 3 x 10^9 stat coulomb,  1 absolute coulomb= 10C, 1 faraday = 96500C Specific property of charge: - Charge is a scalar quantity . - Charge is transferable. - charge is always associated with mass. - Charge is quantised. Q=ne - Charge is conserved. - Charge is invariant.

MATTER WAVE :-          In 1924 de-broglie proposed that matter also has a dual nature just like radiation. His hypothesis about the dual nature of matter was base on following observations.   I) The whole universe is composed of matter and electromagnetic radiation.   II) The nature loves symmetry . As the radiation has dual nature, matter should also possess dual nature.          According to de-broglie, a wave is associated with every moving material particles. These waves are called de-broglie waves or matter waves.     According to quantum theory, energy of a photon is given bye                   E= hv   Where h is Planck's constant and v is frequency of radiation. Relativistic energy of a particle is given by Sine rest mass of photon is zero i.e mo= 0 Then  E= pc            hv= pc  Momentum o...

Radioactivity: The uranium salt emitted the rays spontaneously.The phenomenon of spontaneous emission of radiations by heavy elements is called Radioactivity . Properties of nuclear radiation: 1. Properties of Alpha(α) rays: - Alpha(α) particles is a helium nucleus consisting of two protons and two neutrons. - The velocity of α- particles ranges from 1.4 x 10^7 m/s to 2.05 x 10^7 m/s. -They are deflected by electric and magnetic fields. - Alpha (α) particles produce fluorescence in substance like zinc sulphide and barium platinocyanide. - They are massive particles and hence easily stopped by an aluminium sheet of only 0.02mm thick or even by ordinary sheet of paper. - They have great ionising power. Each α-particles produces thousands of ions pairs in a gas before being absorbed. - They get scattered while passing through this metal foils. - They affect a photographic plate. - They can produce artificial radioactivity in certain elements and can produce nuclea...

Planks quantum Theory:    To explain the black body radiation Plank assumed that the energy of oscillatory particles should be discrete rather then continues. According to him the oscillators can emit or absorb energy in the packets. - Energy carried by each photon is hv . - E=n h v where n= 1,2,3,..... h is a planks constant.The value of h=6.625 × 10^−34 J.s Thus photons are particles of electromagnetic radiation emitted by source of radiation . The important characteristics of photons are: 1. Energy of photons is E=hv = hc/λ, where v is frequency of photons and c is velocity of radiation. 2. All photons travel with the same speed which is equal to speed of light i.e c =3 x 10^8 m/s. 3. The speed of photons is different in different media. 4. Photons of different wavelengths (λ) move with different speeds in the same medium. 5 .The photons travels in straight lines. 6 .Rest mass of photon is zero. 7. Momentum of a photon= Mass x velocity ...

Black body Radiation: Every body emits energy in the form of wave due to its temperature these radiation are known as Thermal radiation . -A perfectly blackbody is one which absorbed heat radiation of all wavelength incident on it. -It neither reflects nor transmits any of the incident radiation and therefore,appears black. - When a black body is heated its emits radiation which are known as black body radiation.

Photoelectric effect: when light is incident on a metal surface then electrons are emitted from it. This phenomena is called photoelectric effect.The emitted electrons are called photoelectrons. Laws of photoelectric emissions : 1. The emission of photo-electrons takes place only when the frequency of incident radiation is above certain critical value of that metal.This critical value is called threshold frequency . 2 . The emission of photo-electrons starts as soon as the light falls on metal surface i.e.the photoelectric emission is instantaneous. 3 . The maximum kinetic energy with which the photo-electrons are emitted from a metal surface is independent of the intensity of the light and only depends upon the frequency. 4 . For a given frequency, the number of photo-electrons emitted is directly proportional to the intensity of incident light . 5 .The energy distribution of the photo-electron is independent of the intensity of the incident ...

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