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1. UNIT 2 AP-2 15FORTEENS MUST DO TOPICS MOST REPEATED QUESTION BEST NOTES AND STUDY MATERIAL

2. DISTRIBUTION LAWS Every matter is assembly of number of microscopic particles. The actual interaction of individual particles cannot be described. But after considering the distribution of individual particles in different possible states with help of distribution laws. THERE ARE THREE DISTRIBUTION LAWS

3. 1. MAXWELL BOLTZMAN (M-B) DISTRIBUTION LAW Identical, indistinguishable particles having any spin. EX- Molecules of gas. It does not follow paulis exclusion principle. They follow symmetric wave function. Mathematical form

4. 2. BOSE EINSTEIN (B-E) DISTRIBUTION LAW Identical, indistinguishable particles having zero or integral spin EX- BOSONS (Photon (spin-1), Phonon (spin-0) ) It does not follow paulis exclusion principle. They follow symmetric wave function. Mathematical form:

5. 3. FERMI DIRAC (F-D) DISTRIBUTION LAW Identical, indistinguishable particles having odd half integral spin. EX- FERMIONES (Electrons) It follow paulis exclusion principle. They follow anti-symmetric wave function. Mathematical form:

6. BLACK BODY A black body is a perfect absorber and absorbs all the radiation incident on it and can emit all the the radiation on heating it. Ferry design a black body which can absorb 97% of radiation incident on it and can emit 97% radiation on heating it

7. BLACK BODY RADIATION SPECTRUM The energy emitted per second from black body increases on increasing the temperature of black body. There is a non-uniform distribution of energy in black body Acc. To Weins displacement law maximum wavelength is inversely propotional to temperature. λ max= 1/ T Acc. to stefans law energy emitted is fourth power of T E=T4

8. Failure of classical theory to explain black body radiation spectrum

9. PLANCK’S RADIATION FORMULA Acc. to placks quantum theory radiation consist of a number of tiny particles these particles are known as photons. These photons have discrete energies not continuous energies. Plancks black body formula is: u(v) dv = 8 π h ν 3 / c 3  × 1/( e h ν/ kT -1) where  c  is the  speed of light ,  k  is the  Boltzmann constant ,  T  is the  absolute temperature , and  v  is the frequency .

10. PLANCK’S RADIATION FORMULA AT LOW FREQUENCY

11. PLANCK’S RADIATION FORMULA AT HIGH FREQUENCY

12. MAXWELL BOLTZMAN (M-B) SPEED DISTRIBUTION LAW FOR IDEAL GAS

13. FREE ELECTRON THEORY Free electron theory is of 2 types: Classical free electron theory Quantum free electron theory

14. Classical free electron theory Electron moves freely in metals in all directions. Electrons behaves as a gas molecules in container which obey laws of kinetic theory of gases. Average energy per electron at a temperature T is 3KT /2. Electric conduction is due to free electron only . DRAWBACKS It could not explain the specific heat of metal. It could not explain mean free path of electron. It could not explain phototelectric effect

15. Quantum free electron theory Electrons move freely in a constant potential within boundries of metal Electrons are filled in different energy levels acc. to Pauli’s Exclusion Principle. The energy values of free electrons are quantized. The attraction between ions and electrons and repulsion between electrons are ignored The possible energy values can be calculated by schrodinger wave equation.

16. DRAWBACKS It is unable to explain the metallic properties of certain crystals It is unable to explain difference between metal, insulators and semiconductors. Unable to explain the positive value of half coefficient.

17. SPECIFIC HEAT It is defined as the amount of energy required to raise the temperature of 1kg substance by 1K.

18. FERMI ENERGY Fermi energy is a concept in quantum mechanics that usually refers to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature. .