Q1 · June 2019 · 2 marks
A certain system of non interacting particles has the single-particle partition function f = A\frac{T^m}{V} where A is some constant. The average energy per particle will be
- (a) mkT
- (b) AkT
- (c) kT/m
- (d) kT/A
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Answer: (a)
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Q2 · June 2013 · 2 marks
The allowed transition among the following is
- (a) {}^3\mathrm{F}_4 \rightarrow {}^3\mathrm{D}_3
- (b) {}^3\mathrm{F}_4 \rightarrow {}^1\mathrm{D}_3
- (c) {}^3\mathrm{F}_4 \rightarrow {}^3\mathrm{P}_4
- (d) {}^3\mathrm{F}_4 \rightarrow {}^3\mathrm{D}_2
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Answer: (a)
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Q3 · June 2019 · 2 marks
The rotational partition function is expected to be the smallest for the molecule, among the following
- (a) \mathrm{H_2}
- (b) \mathrm{Li_2}
- (c) \mathrm{N_2}
- (d) \mathrm{F_2}
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Answer: (a)
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Q4 · June 2019 · 2 marks
The difference between standard molar entropies of two mono-atomic gases (A) and (B) \left(S_{\mathrm{m},\mathrm{A}}^{0}-S_{\mathrm{m},\mathrm{B}}^{0}\right) at a given temperature is (given that the molar mass of (A) is twice the molar mass of (B)
- (a) \frac{3}{2}R\ln 2
- (b) R\ln 2
- (c) \frac{5}{2}R\ln 2
- (d) \frac{7}{2}R\ln 2
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Answer: (a)
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Q5 · Dec 2019 · 2 marks
Consider a two-level system in which the excited state, separated from the ground state by energy \epsilon, is doubly degenerate. The fraction of the molecules in the excited state, as T \rightarrow \infty is
- (a) \frac{1}{2}
- (b) -\frac{1}{2}
- (c) \frac{2}{3}
- (d) 1
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Answer: (c)
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Q6 · Dec 2019 · 2 marks
The molar residual entropy (in \mathrm{J\,K^{-1}}) of solid OCS would be closest to
- (a) 0
- (b) 2.9
- (c) 5.8
- (d) 8.7
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Answer: (c)
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Q7 · Dec 2018 · 2 marks
The translational partition function for Ar confined to a volume of 1L at 300K, having thermal wavelength of 1.60 \times 10^{11}\ \mathrm{m}, is closest to :
- (a) 24.4 \times 10^{29}
- (b) 2.44 \times 10^{29}
- (c) 0.244 \times 10^{29}
- (d) 244 \times 10^{29}
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Answer: (b)
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Q8 · Dec 2017 · 2 marks
Four distinguishable molecules are distributed in energy level E1 and E2 with degeneracy of 2 & 3 respectively. Number of microstates with 3 molecules in in energy level E1 and E2 is
- (a) 4
- (b) 12
- (c) 96
- (d) 192
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Answer: (c)
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Q9 · June 2017 · 2 marks
The first excited state ({}^{2}\mathrm{P}_{1/2}) of fluorine lies at an energy of 400\ \mathrm{cm^{-1}} above the ground state ({}^{2}\mathrm{P}_{3/2}). The fraction of Fluorine atoms in the first excited state at k_BT = 420\ \mathrm{cm^{-1}} is close to
- (a) \frac{1}{1+e}
- (b) \frac{1}{2+e}
- (c) \frac{1}{1+4e}
- (d) \frac{1}{1+2e}
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Answer: (d)
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Q10 · Dec 2017 · 2 marks
The term symbol for the ground state of a metal ion is {}^{3}\mathrm{P}_{2}. The residual entropy of a crystal of a salt of this metal ion at 0 K is :
- (a) k_B \ln 1
- (b) k_B \ln 3
- (c) k_B \ln 5
- (d) k_B \ln 7
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Answer: (d)
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Q11 · June 2016 · 2 marks
The single – partition translational partition function (f) for an ideal gas in a fixed volume V depends on the thermal Broglie wave function \lambda^{\mathrm{th}} as f\sim(\lambda^{\mathrm{th}})_n where :
- (a) n=3
- (b) n=1
- (c) n=-1
- (d) n=-3
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Answer: (d)
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Q12 · Dec 2016 · 2 marks
The weight of configuration with two ups and three down spins in a system with five spin \frac{1}{2} particles is
- (a) 120
- (b) 60
- (c) 20
- (d) 10
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Answer: (d)
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Q13 · Dec 2016 · 2 marks
Partition function of a one - dimensional oscillator having equispaced energy level with energy spacing equal to \boldsymbol{k}_{\boldsymbol{b}} \boldsymbol{T} and zero ground energy is
- (a) e
- (b) 1/(e-1)
- (c) \mathrm{e} /(\mathrm{e}-1)
- (d) 1 /(e+1)
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Answer: (c)
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Q14 · Dec 2015 · 2 marks
Though a constant shift of energy levels of a system changes the partition function, the properties that do not change are
- (a) average energy, entropy and heat capacity
- (b) average energy and entropy
- (c) average energy and heat capacity
- (d) entropy and heat capacity
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Answer: (d)
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Q15 · Dec 2014 · 2 marks
Identify the speed distribution functions of Ne, Ar and Kr with the curves in the figure above: 
- (a) Ne-A, Ar-B, Kr-C
- (b) Ne-B, Ar-C, Kr-A
- (c) Ne-C, Ar-B, Kr-A
- (d) Ne-C, Ar-A, Kr-B
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Answer: (c)
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Q16 · Dec 2014 · 2 marks
The number of microstates that are possible, when two particles are distributed in four states such that the resulting wave functions are antisymmetric with respect to exchange of the particles, is :
- (a) 16
- (b) 12
- (c) 8
- (d) 6
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Answer: (d)
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Q17 · Dec 2014 · 2 marks
When T \rightarrow \infty, value of the single-particle partition function will be (given : degeneracy of level j = g_j) :
- (a) 1
- (b) g_0
- (c) \Sigma_j g_j
- (d) 1/\Sigma_j g_j
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Answer: (c)
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Q18 · Dec 2014 · 2 marks
The probability of finding the harmonic oscillator in the energy level n = 1 is (neglect zero point energy and assume h\nu = k_BT)
- (a) e
- (b) e^2
- (c) 1 - e^2
- (d) e^{-2}(e-1)
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Answer: (d)
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Q19 · Dec 2014 · 2 marks
Identify the speed distribution functions of \mathrm{Ne}, \mathrm{Ar} and Kr with the curves in the figure above:
- (a) Ne-A, Ar-B, Kr-C
- (b) Ne-B, Ar-C, Kr-A
- (c) Ne-C, Ar-B, Kr-A
- (d) Ne-C, Ar-A, Kr-B
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Answer: (c)
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Q20 · Dec 2013 · 2 marks
The number of ways in which four molecules can be distributed in two different energy levels is :
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Answer: (c)
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Q21 · June 2013 · 2 marks
A system has 100 degenerate energy levels and 100 bosons are kept in it. Find the entropy of the system at equilibrium
- (a) 10^{-2}\,k_b
- (b) 10^{2}\,k_b
- (c) 460.0\,k_b
- (d) 4.606\,k_b
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Answer: (b)
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Q22 · Dec 2012 · 2 marks
Calculate the total number of microstates for 6 identical particles with their occupation numbers \{1, 2, and 3\} in three states is
- (a) 6
- (b) 12
- (c) 60
- (d) 720
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Answer: (c)
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Q23 · June 2012 · 2 marks
The relative population in two states with energies E_1 and E_2 satisfying Boltzmann distribution is given by n_1/n_2 = (3/2)\exp[-(E_1 - E_2)/k_bT]. The relative degeneracy g_2/g_1 is:
- (a) 2
- (b) 2/3
- (c) 3/2
- (d) 3
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Answer: (b)
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Q24 · Dec 2012 · 2 marks
The rotational partition function of \mathrm{H_2} is :
- (a) \sum_{J=0,1,2\ldots}(2J+1)e^{-\beta hcBJ(J+1)}
- (b) \sum_{J=1,3,5\ldots}(2J+1)e^{-\beta hcBJ(J+1)}
- (c) \sum_{J=0,2,4\ldots}(2J+1)e^{-\beta hcBJ(J+1)}
- (d) \frac{1}{4}\left[\sum_{J=0,2,4\ldots}(2J+1)e^{-\beta hcBJ(J+1)} + 3\sum_{J=1,3,5\ldots}(2J+1)e^{-\beta hcBJ(J+1)}\right]
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Answer: (d)
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Q25 · June 2011 · 2 marks
The term symbol for the ground state of nitrogen atoms is
- (a) {}^{3}P_{0}
- (b) {}^{4}P_{3/2}
- (c) {}^{1}P_{1}
- (d) {}^{4}S_{3/2}
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Answer: (a)
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Q26 · Dec 2011 · 2 marks
P_A and P_B denote the populations of two energy states E_A and E_B and E_A > E_B. The correct statement when the temperature T_1 > T_2 is
- (a) P_A(T_1) > P_B(T_1), P_A(T_2) < P_B(T_2) and (P_A/P_B)_{T_1} > (P_A/P_B)_{T_2}
- (b) P_A(T_1) < P_B(T_1), P_A(T_2) > P_B(T_2) and (P_A/P_B)_{T_1} > (P_A/P_B)_{T_2}
- (c) P_A(T_1) < P_B(T_1), P_A(T_2) < P_B(T_2) and (P_A/P_B)_{T_1} > (P_A/P_B)_{T_2}
- (d) P_A(T_1) < P_B(T_1), P_A(T_2) < P_B(T_2) and (P_A/P_B)_{T_1} < (P_A/P_B)_{T_2}
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Answer: (c)
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Q27 · Dec 2011 · 2 marks
A system consisting of 4 identical and distinguishable particles, each possessing three available states of 1,2 and 3 units, has 10 units of energy. The number of ways, W, in which these conditions are satisfied is :
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Answer: (d)
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