6. Which set of the operators or physical quantities do NOT satisfy the Heisenberg uncertainty principle?
(A) Angular momentum operators $\hat{\Gamma}_{\mathrm{y}} = -\mathrm{i}\hbar \left(\cos \phi \frac{\partial}{\partial\theta} -\cot \theta \sin \phi \frac{\partial}{\partial\phi}\right)$ and $\hat{L}_{z} = -\mathrm{i}\hbar \frac{\partial}{\partial\phi}$
(B) Frequency $(\nu)$ and time $(t)$
(C) Momentum $(P)$ and position $(x)$
(D) Operators $\hat{I} = 5$ and $\hat{J} = \int_{1}^{\infty} dx$

7. Which of the following quantum mechanical model does NOT have the zero-point energy? (A) Particle in a box with finite potential wells (B) Rigid rotor (C) Harmonic oscillator (D) Quantized electromagnetic field

8. Which of the following molecule may NOT show a rotational Raman spectrum? (A) $\mathrm{N}_2$ (B) $\mathrm{CO}_{2}$ (C) $\mathrm{H}_{2} \mathrm{O}$ (D) $\mathrm{CH}_{4}$

9. Scientists used ultrafast X-ray pulses to directly visualize the DNA photorepair process. The probability of bond-rearrangement events was observed to increase gradually over a timescale of approximately 500 ns. Which of the following statements is incorrect? (A) Molecular bond elongation occurs on a timescale of approximately 500 ns. (B) Molecular bond elongation occurs on a timescale of approximately 500 fs. (C) Although molecular bond vibrations occur on ultrafast timescales, the concentration of reaction products may require a much longer time to increase to a detectable level. (D) The presence of multiple reaction barriers allows reactant molecules that have crossed a barrier to return via reverse reactions.

10. In a consecutive reaction $A \rightarrow B \rightarrow C$ concentration of the intermediate will be small relative to the starting concentration of A if (A) the rate constant for the first step is larger than that for the second, (B) the rate constant for the second step is larger than that for the first, (C) very few products have formed, (D) nearly all the reactant has disappeared.

11. If a system at equilibrium is perturbed in the forward direction, the system will approach equilibrium with a rate determined by (A) the forward rate constant (B) the reverse rate constant (C) a combination of the two (D) neither

12. What is the physical meaning of $\Delta A$ in thermodynamics? (T: temperature; V: volume)(A) Maximum heat at constant T and V (B) Maximum non-expansion work at constant T and V(C) Maximum work at constant T and V (D) Maximum work at constant T

13. $\left(\frac{\partial \left(\frac{A}{T}\right)}{\partial \left(\frac{1}{T}\right)}\right)_V = ?$(A) $G$ (B) $H$ (C) $U$ (D) $S$

14. What is the expression of entropy change $(\Delta S)$ for the isothermal reversible expansion at temperature $T$ from $V_{1}$ to $V_{2}$ of $n$ moles of a van der Waals gas?(A) $nRT\ln \frac{V_1 - nb}{V_2 - nb} + an^2\left(\frac{1}{V_1} -\frac{1}{V_2}\right)$ (B) $-nR\ln \frac{V_1 - nb}{V_2 - nb} -\frac{an^2}{T}\left(\frac{1}{V_1} -\frac{1}{V_2}\right)$(C) $nR\ln \frac{V_1 - nb}{V_2 - nb} +\frac{an^2}{T}\left(\frac{1}{V_1} -\frac{1}{V_2}\right)$ (D) $-nRT\ln \frac{V_1 - nb}{V_2 - nb} -an^2\left(\frac{1}{V_1} -\frac{1}{V_2}\right)$

15. The equation of $C_{P,m} - C_{V,m}$ can be expressed in terms of $V_{m}, T,$ and the gas constants $R, a$ and $b$ as follows: $C_{P,m} - C_{V,m} = R / \left(\Gamma - \frac{\Theta a(V_m - b)^\Phi}{RTV_m^\Omega}\right)$ , where $\Gamma, \Theta, \Phi$ and $\Omega$ are real integers. Which of the description about $\Gamma, \Theta, \Phi$ and $\Omega$ is correct? (A) $\Gamma \neq \Omega$ (B) $\Theta \neq \Phi$ (C) $\Theta = \Phi = \Omega = 1$ (D) $\Omega = \Phi$

16. The rate equation of $A^{*}$ is (A) $[A^{*}] = [A]_{0}e^{-(k_{1} + k_{2})t}$ ; (B) $[A^{*}] = [A^{*}]_{0}e^{-(k_{3})t}$ ; (C) $[A^{*}] = [A^{*}]_{0}e^{-(k_{1} + k_{2} + k_{3})t}$ ; (D) $[A^{*}] = [A]_{0}e^{-(k_{1} + k_{2} + k_{3})t}$

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