112年 - [無官方正解]112 國立嘉義大學_碩士班招生考試試題_應用化學系：物理化學#144354

1. What is the slope when we plot the ln k verses 1/T, and where k is the rate constant? (hint: using the Arrhenius equation) (A) $-\frac{E_a}{R}$ (B) Equilibrium constant (C) Joule coefficient (D) Planck constant.

2. Suppose the sun's surface temperature is 5800 K, and the peak wavelength of its emission is 500 nm. What is Venus's peak thermal radiation wavelength (surface temperature is about 730 K)? (A) 400 nm (B) 4,000 nm (C) 1,000 nm (D) 10,000 nm.

3. What is the unit of the rate constant of a first-order reaction? (A) no unit (B) \(t^{-1}\) (C) \(M^{-1}t^{-1}\) (D) \(M^{-2}t^{-1}\)

4. Which of the following molecules is not a greenhouse gas? (A) CO₂ (B) C₂H₂ (C) O₂ (D) CO.

5. What is the **selection rule** for particle-in-one-dimension-box? (A) \(\Delta S=0\) (B) \(\Delta J=0, \pm 1\)
(C) \(\Delta V = \pm 1\) (D) \(\Delta n = \pm 1, \pm 3, \pm 5,....\)

6. Which one of the following Maxwell relations can be derived from one of the Gibbs equations \( dG = -SdT + VdP \)? (A) \( \left(\frac{\partial T}{\partial P}\right)_S = \left(\frac{\partial V}{\partial S}\right)_P \) (B) \( \left(\frac{\partial V}{\partial T}\right)_P = -\left(\frac{\partial S}{\partial P}\right)_T \) (C) \( \left(\frac{\partial P}{\partial S}\right)_V = -\left(\frac{\partial T}{\partial V}\right)_S \) (D) \( \left(\frac{\partial S}{\partial V}\right)_T = \left(\frac{\partial P}{\partial T}\right)_V \)

7. Which of the following molecules has unpaired electron(s) in the electronic ground state? (A) O₂ (B) N₂ (C) H₂ (D) Cl₂.

8. The term symbol for the ground electronic state of O₂ is (A) ¹Σ_g⁺ (B) ³Σ_g^- (C) ¹Π_u (D) ¹Π_g

9. Which of the following is an eigenfunction of the operator $\hat{A} = \frac{\partial^2}{\partial r^2}$ (A) $e^{-r}$ (B) $e^{-r^2}$ (C) $\frac{1}{r}e^{-r}$ (D) $re^{-r}$

10. What is the point group of C₂H₄? (A) C_2v (B) C_2h (C) D_2h (D) D_2d.