Statistical Mechanics Test Questions 6u2n3b

Statistical Mechanics Test/ Dr. Abhijit Kar Gupta, [email protected]

Tick the correct answer: 1.

10x1=10

The average energy of a harmonic oscillator in 3-dimension is (a) , (b) 3 , (c) , (d) none

2. The following FD-distributions correspond to two different temperatures, of these is correct? 𝑇

and

. Which one

𝑇

(a)

,

(b)

,

(c)

,

(d) Can not be said definitely

3. The relation between Fermi energy and density of electrons: (a) , (b) , (c) , (d) 4. If the energy of a particle can be either 1, 2, 3, 4, 5 or 6 units with the probabilities 1/21, 2/21, 3/21, 4/21, 5/21, 6/21 respectively, the average energy of the particle is (a) 4.5, (b) 5/21, (c) 5.1, (d) 4.3 5. If the energy of a quantum harmonic oscillator is function of the system of oscillators is (a)

,

,

(b)

(c)

,

,

, the partition

(d)

6. If be the partition function of a system of particles, the average energy is written as (a) ̅ , (b) ̅ , (c) ̅ , (d) ̅ 7. If be the ratio of the probability that the two particles are found in the same state to the probability that two particles belong to different states, then the ratio =? (a) , (b) 1 : 0 : 2 , (c) 1 : 1 : 2, (d) 1 : : 0 8. Two classical particles have energy states with degeneracies 1, 2, 4 respectively. How many total configurations possible for this system? (a) 16, (b) 21, (c) 20, (d) 18 9. Consider MB distribution. How can the fluctuation in velocity be related to temperature? (a) , (b) , (c) , (d) 10. The relation between the number of microstates molecules in a volume is related to energy : (a)

,

(b)

,

(c)

for an ideal gas of ,

(d)

monatomic

Statistical Mechanics Test/ Dr. Abhijit Kar Gupta, [email protected]

Answer is given at the end! yourself.

Ans. 1(b), 2(b), 3(c), 4(d), 5(c), 6(c), 7(a), 8(b), 9(a), 10(d)