複選題

15. 元素 X 的電子組態[36Kr]4d¹⁰5s²5p²，下列選項關於此元素的敘述哪些正確？
(A)與碳在同一族
(B)位於週期表的第四列
(C)為一過渡金屬
(D)可與氯結合成 XCl₄ 的分子
(E)每個原子中有 50 個質子。

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複選題33. 元素X的電子組態為[36Kr] 4d105s25p2，則關於此元素敘述正確的有？ (A)與碳在同一族 (B)位於週期表的第四列 (C)為一過渡金屬 (D)可與氯結合成XCl4的分子 (E)每個原子中有50個質子

1. The fine structure constant is defined as α ≡ . The unit of α is the same as: (A) Length (B) Energy (C) Length²/Time (D) 1/Time (E) No unit

2. A student dropped a ball from the roof of a building. After 11.5 seconds, she heard it hitting the ground. Assuming that the speed of sound is 340 m/s, which of the following is closest to the height of the building? (A) 30 m (B) 100 m (C) 200 m (D) 500 m (E) 800 m

3. A solid sphere of mass m and radius r moves along a track with a circular loop of radius R1 as shown in following picture. It is released at height h. Assuming that the track has no friction, the ball thereforeslides down without rotation. Do not ignore the finite size of the sphere, what is the minimal value of h such that the sphere remains on the track at all times? (A) 2.5R − 1.5r (B) 2R − r (C) 2.5R (D) 2R + r (E) 2R − 1.5r

4. Same arrangement as in problem 3. If the sphere is released at a height h = 3R, what is the force exerted by the track at the top of the loop? (A) 2mg (B) mg (C) 0.5mg (D) mg(R + 3r)/(R − r) (E) mg(R + r)/(R − 4)

5. Same as problem 3, except now the track surface is rough and the sphere rolls without sliding. What is the minimal value of h such that the sphere remains on the track? (A) 2.5R + 0.7r (B) 2.7R + 1.7r (C) 2.7R − 1.7r (D) 2.5R − 1.5r (E) 2.5R + 1.5r

6. In a photoelectric effect experiment, a light ray of intensity I and frequency ν shines on a metal surface. The resulting photo current is j, and the highest energy of the photo electrons is E. Which of the following relations describes the photoelectric effect. (A) j ∝ I (B) j = hν + W (C) E = hI + W (D) E = hν + W (E) E ∝ I. Here h and W are constants.

7. A Carnot engine operated between temperatures TH and TL. What is the entropy gain per cycle? (A) 0 (B) kB N TH (C) (D) (E) kB N(TH − TL). Here kB is the Boltzmann constant, and N is the number of gas molecules.

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