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複選題28. The energy of a particle in a 3D cubic box is given by the formula: $$ E_{n_x, n_y, n_z} = \frac{h^2}{8mL^2} \left(n_x^2 + n_y^2 + n_z^2\right) $$ where $h$ is Planck's constant, $m$ is the mass of the particle, $L$ is the dimensions of the box, and $n_x$, $n_y$, and $n_z$ are the quantum numbers. Which of the following statements are correct? (A) The degeneracy of the ground state is one (B) The degeneracy of the first excited state is three (C) The energy of the first electronic absorption band is $\frac{3h^2}{8mL^2}$ (D) The degeneracy of the excited state resulting the broad emission band (E) Without a zero-point energy

複選題27. There are three methods for hydrogen production (1) Methane pyrolysis: $\mathrm{CH_4(g)} \rightarrow \mathrm{C(s)} + 2 \mathrm{H_2(g)}$; $\Delta \mathrm{H} = +76 \mathrm{kJ}$, corresponding to $+38 \mathrm{kJ}$ per mole of $\mathrm{H_2}$ produced. (2) Water electrolysis: $2 \mathrm{H_2O(l)} \rightarrow \mathrm{O_2(g)} + 2 \mathrm{H_2(g)}$; $\Delta \mathrm{H} = +572 \mathrm{kJ}$, corresponding to $+286 \mathrm{kJ}$ per mole of $\mathrm{H_2}$ produced. (3) Steam methane reforming: $\mathrm{CH_4(g)} + 2 \mathrm{H_2O(g)} \rightarrow \mathrm{CO_2(g)} + 4 \mathrm{H_2(g)}$; $\Delta \mathrm{H} = +252 \mathrm{kJ}$, corresponding to $+63 \mathrm{kJ}$ per mole of $\mathrm{H_2}$ produced. Based solely on the reaction enthalpies $(\Delta \mathrm{H})$, methane pyrolysis [method (1)] appears to be the most energy-efficient pathway for hydrogen production. However, this conclusion is misleading in practice and does not adequately represent the true energetic and technological challenges of the process. Which of the following statements correctly explain the reasons? (A) Although the net enthalpy requirement is only $38\mathrm{kJ}$ per mole of $\mathrm{H}_{2}$, a much higher activation energy must be overcome to cleave the strong C-H bonds in methane. (B) Non-catalytic methane pyrolysis requires temperatures above approximately $1200^{\circ}\mathrm{C}$, with activation energies typically in the range of $300 - 420\mathrm{kJ / mol}$. (C) Catalytic methane pyrolysis employing metal (e.g., Ni, Fe, Cu) or carbon catalysts can lower the required operating temperature to approximately $600 - 900^{\circ}\mathrm{C}$ and reduce the activation energy to about $150 - 200\mathrm{kJ / mol}$. (D) In methane pyrolysis reactors, heat transfer to methane is generally less efficient than in steam methane reforming [method (3)], which benefits from the use of high-temperature water vapor as an effective heat-transfer medium. (E) In [method 3], the total bond enthalpy of the products is less than that of reactants.

複選題26. If the fluorescence quantum yield $(\varnothing_{f})$ of anthracene is $10\%$, and the fluorescence lifetime is $50\,\mathrm{ns}$, $k_{r}$ is the radiative rate constant, and $k_{nr}$ is the non-radiative rate constant. Which of the following are TRUE? (A) $k_{r} = 2 \times 10^{6}\,\mathrm{sec}^{-1}$ (B) $k_{r} = 2 \times 10^{7}\,\mathrm{sec}^{-1}$ (C) $k_{nr} = 2 \times 10^{6}\,\mathrm{sec}^{-1}$ ![img-0.jpeg](img-0.jpeg) 注意:背面有試題 台灣聯合大學系統115學年度碩士班招生考試試題 類組:化學類 科目:物理化學(1004) 共 6 頁第 6 頁 (D) $k_{nr} = 1.8 \times 10^{7} \sec^{-1}$ (E) $k_{nr} = 9k_{r}$

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54. 「RFID」這個名詞,中文稱為: (A)自動檢索系統 (B)無線射頻辨識系統 (C)電腦網路查詢 系統 (D)數位電子資訊系統。

60 下列哪些藥物具有antagonism of neuromuscular blockade的作用? (1)4-aminopyridine (potassium channel-blocking agent) (2)Edrophonium (acetylcholinesterase inhibitor) (3)Sugammadex (γ-cyclodextrin derivatives) (A) 只有 1 (B) 只有 2 (C) 只有 3 (D) 2 + 3 (E) 1 + 2 + 3

1 下列何人提出基本規範之學說,作為法律強制力之形式基礎? (A)凱爾生(H. Kelsen) (B)薩維尼(Savigny) (C)黑格爾(Hegel) (D)哈特(H. A. L. Hart)

3. 下列何者為擴散性教學革新最重要的機制? (A) 善用非正式團體 (B) 激起對話交流 (C) 強化目標承諾 (D) 衝突協調

9. 小陳經營一家數位印刷廠。在短期內,他擁有一台價值100萬元的專業印刷機;在長期下,他可以決定是否要搬到更大的廠房或增加更多自動化設備。請問下列關於小陳經營成本的敘述,何者正確?(A)在短期內,如果小陳完全不生產,他的總成本(TC)將會等於零 (B)當小陳增加產量使得邊際成本(MC)高於平均成本(AC)時,代表他的平均成本正在下降 (C)長期平均成本曲線(LAC)是由無數條短期平均成本曲線(SAC)最低點的連線所組成 (D)若小陳擴大廠房規模後,發現每本雜誌的平均印刷成本從50元降為40元,代表他處於規模經濟階段。

10. 下列何者屬於政府財政政策中的主動性財政政策?①失業保險制度 ②調降證券交易 ③採取累進所得稅 ④增加公共支出 ⑤發放全民振興消費券 ⑥調整遺產稅免稅額。(A)①③⑤ (B)②④⑤⑥ (C)②④⑤ (D)①②③⑥。