109年 - [無官方正解]109 國立嘉義大學_碩士班招生考試試題_應用化學系：物理化學#146840

1. Given that dH = TdS + Vdp and that G = H - TS，which of the following is true? (A) dG = TdS - VdP (B) dG = dH - SdT (C)dG = -SdT + Vdp (D) dG = dH - TdS

2. Which of the following is zero for an ideal gas? (A) $\left(\frac{\partial H}{\partial T}\right)_p$ (B) $\left(\frac{\partial U}{\partial T}\right)_v$ (C) $\left(\frac{\partial V}{\partial T}\right)_p$ (D) $\left(\frac{\partial H}{\partial p}\right)_T$

3. What is the wavelength of the photon emitted from 2p to 1s of a hydrogen atom? (The Rederberg constant is $1.097 \times 10^5 cm^{-1}$) (A) 91.1 nm (B) 121.6 nm (C) 364.6 nm (D) 486.1 nm

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

5. Which of the following molecules has unpaired electron(s) in the electronic ground state? (A) O$_2$ (B) N$_2$ (C) H$_2$ (D) Cl$_2$

6. What is the orbital angular momentum of an electron in the 4d orbital? (A) $\sqrt{2} \hbar$ (B) $\sqrt{6} \hbar$ (C) $\sqrt{12} \hbar$ (D) $\sqrt{20} \hbar$

7. How many vibrational modes does an SO$_2$ molecule have? (A) 3 (B) 4 (C) 5 (D) 6

（二）計算題及問答題
1. $A^* \xrightarrow{k_f} A + h\nu$，$A^* \xrightarrow{k_{non-rad}} A + heat$，where $k_f$ and $k_{non-rad}$ are the rate constants of fluorescence and non-radiation processes, respectively. Find the fluorescence quantum yield ($\Phi_f$) in this system. (4 分)