110年 - [無官方正解]110 國立嘉義大學_碩士班招生考試試題_應用化學系：物理化學#146467

1. What is the orbital angular momentum of an electron in the 3p orbital? (3%) (A) \( \sqrt{2} \hbar \) (B) \( \sqrt{6} \hbar \) (C) \( \sqrt{12} \hbar \) (D) \( \sqrt{20} \hbar \)

2. Which one of the following Maxwell relations can be derived from one of the Gibbs equations, \( dU = TdS - PdV \)? (3%) (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) \( \left( \frac{\partial S}{\partial V} \right)_T = \left( \frac{\partial P}{\partial T} \right)_V \)

3. Which of the following partial derivatives is not zero for an ideal gas? (3%) (A) \( \left( \frac{\partial H}{\partial P} \right)_T \) (B) \( \left( \frac{\partial U}{\partial V} \right)_T \) (C) \( \left( \frac{\partial S}{\partial T} \right)_P \) (D) \( \left( \frac{\partial T}{\partial P} \right)_H \)

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

5. An electron in which of the following orbitals of the hydrogen atom has the largest
average distance from the nucleus? (3%)
(A)1s (B) 2 p (C) 3d (D) 4s

6. The ionization energy for the hydrogen atom at the ground state is 13.6 eV. What is
the wavelength of the light emitted from 2p orbital to 1s orbital Li²⁺ ion? (3%)
(A) 13.5 nm (B) 30.4 nm (C) 121.6 nm (D) 410 nm

7. How many vibrational modes does a C₂H₂ molecule have? (3%)
(A) 5 (B) 6 (C) 7 (D) 8

1.(a) Does CO₂ have IR absorption (2%)? (b) Why (2%)?