Practice Statistical Physics Questions and Answers.

**Statistical Physics Questions and Answers**

*Q1. Two particle are said to be distinguishable when*

*(a) the average distance between them is large compared to their de Broglie wavelength**(b) the average distance between them is small compared to their de Broglie wavelength**(c) they have overlapping wavepackets**(d) their total wave function is symmetric under particle exchange*

*Q2. Which of the following relations between the particle number density n and temperature T must hold good for a gas consisting of non-interacting particles to be described by quantum statistics ?*

*(a) n/T*^{1/2}<< 1*(b) n/T*^{3/2}<< 1*(c) n/T*^{3/2}>> 1*(d) n/T*^{1/2}and n/T^{3/2}can have any value.

**Q3. The number of possible ways to distribute 4 classical particles in 5 energy states is **

*(a)*^{5!}/_{4!}*(b)*^{4!}/_{5!}*(c) 5*^{4}*(d) 4*^{5}

**Q4. The number of possible ways in which 5 identical bosons cam be distributed in 4 energy states is :**

*(a)*^{8!}/_{5! 3!}*(b)*^{9!}/_{5! 4!}*(c)*^{9!}/_{4! 4!}*(d)*^{8!}/_{4! 4!}

**Q5. The number of ways in which N identical bosons can be distributed in two energy levels, is **

*(a) N+1**(b) N(N-1)/2**(c) N(N+1)/2**(d) N*

**Q6. A system has energy level E _{o}, 2E_{o}, 3E_{o}, … where the excited states are triply degenerate. Four non-interacting bosons are placed in this system. If the total energy of these bosons is 5E_{o} , the number of microstates is :**

*(a) 2**(b) 3**(c) 4**(d) 5*

**Q7. Consider a gas of three particles with four available states. Find the number of states available if the gas is Bose-Einstein**

*(a) 64**(b) 4**(c) 16**(d) 20*

**Q8. What are the number of possible microstates of 3 out of 7 fermions can be distributed in two energy state with degeneracy 4 and the rest in some other state with degeneracy 5 ?**

- (a)
^{5!}/_{3! 4!} - (b)
^{7!}/_{4! 5!} - (c)
^{4! 5! 7!}/_{3! 4!} - (d)
^{5!}/_{3!}

**Q9. Let N _{MB} , N_{BE} , N_{FD} denote the number of ways in which two particles can be distributes in two energy states according to Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics respectively. Then N_{MB} : N_{BE} : N_{FD}**

*(a) 4 : 3 : 1**(b) 4 : 2 : 3**(c) 4 : 3 : 3**(d) 4 : 3 : 2*

**Q10. Consider a system of two particles A and B. Each particle can occupy one of the three possible quantum states |1⟩ , |2⟩ , and |3⟩ . The ratio of the probability that the two particles are in the same state to the probability that two particles are in different states is calculated for bosons and classical (Maxwell-Boltzmann) particles. They are respectively **

*(a) 1,0**(b)*^{1}/_{2},1*(c) 1,*^{1}/_{2}*(d) 0,*^{1}/_{2}

**Q11. Consider three situations of 4 particles in a one dimensional box of width L with hard walls. In case (i), the particles are fermions , in case (ii) they are bosons, and in case (iii) they are classical. If the total ground state energy of the four particles in these cases are E _{F} , E_{B} , E_{Cl} respectively, which of the following is true ?**

*(a) E*_{F}= E_{B}= E_{Cl}*(b) E*_{F}> E_{B}= E_{Cl}*(c) E*_{F}< E_{B}< E_{Cl}*(d) E*_{F}> E_{B}> E_{Cl}

**Q12. Two identical particles have to be distributed among three energy levels. Let r _{F} , r_{B} and r_{C} represent the ratios of probability of finding two particles so that the finding one particle in a given energy state. The subscripts B, F and C correspond to whether the particle are bosons, fermions and classical particles, respectively. The r_{F} : r_{B} : r_{C} is equal to**

*(a)*^{1}/_{2}: 0 : 1*(b) 1 :*^{1}/_{2}: 1*(c) 1 :*^{1}/_{2}:^{1}/_{2}*(d) 1 : 0 :*^{1}/_{2}

**Q13. Consider two particles and two non-degenerate quantum levels 1 and 2. Level 1 always contains a particle. Hence , what is the probability that level 2 also contains a particle for each of two cases :**

**》(i) when the two particles are distinguishable and》(ii) when the two particles are bosons ?**

*(a) (i)*^{1}/_{2}and (ii)^{1}/_{3}*(b) (i)*^{1}/_{2}and (ii)^{1}/_{2}*(c) (i)*^{2}/_{3}and (ii)^{1}/_{2}*(d) (i) 1 and (ii) 0*

**Q14. The total number of accessible states of N non interacting particles of spin ^{1}/_{2} is**

*(a) 2*^{N}*(b) N*^{2}*(c) 2N*^{N/2}*(d) N*

*Q15. A system comprises of three electrons. There are three single particle energy levels accessible to each of these electrons. The number of possible configurations for this system is*

*(a) 1**(b) 3**(c) 6**(d) 7*

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**Answer Key** (if you find any answer wrong, feel free to Correct us)

**Answer Key**(if you find any answer wrong, feel free to Correct us)

01. | (a) | 06. | (b) | 11. | (b) |

02. | (c) | 07. | (d) | 12. | (d) |

03. | (c) | 08. | (d) | 13. | (c) |

04. | (a) | 09. | (a) | 14. | (a) |

05. | (a) | 10. | (c) | 15. | (d) |