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2. (10 pts) Consider the following set of ions:. To which ones can we apply Bohr's quantized energy formula? Explain your reasoning.

其他申論題

(2)其質量約為靜止質量的幾倍

(3)質子速度與光速的比值(v/c)

7. 一般會使用鉛材料(密度 11.35 g/cm 3)進行 X 光機的輻射防護，請問鉛對 70 keV 光子的半值層(HVL)與什一值層(TVL)各為多少 cm？ (70 keV 光子的質量衰減係數為 2.8 )

1. (10 pts) A star which is 4.3 light-years away from earth. A rocket leaves for the star at a speed of v = 0.95c relative to the Earth. Assume that the Earth and the star are stationary with respect to one another. According to the astronauts, how much did they age (in years) during their journey?

3. (10 pts) Consider a particle in a box (a.k.a. the infinite square well) with a length of L. Calculate the probability that a particle, in the ground state, will be found within the position from L /4 L to 3 L /4.

4. (10 pts) The 2nd bound state (n = 1) wave function of the harmonic oscillator is given by: Is the wave function normalized? Explain your reasoning

5. (10 pts) A lightbulb that is operated at 60 W actually produces about 3 W of visible light. Most of the rest of the energy is heat. Assume the average wavelength of visible light is 550 nm. Evaluate how many visible photons such a lightbulb produce each second.

(a) (5 pts) When a particle with a mass of m is in the well, what are the average values of the lowest kinetic and potential energies?

(b) (5 pts) When a particle with a mass of m is in the well, what is the root-mean- square speed at the first excited state?

(c) (10 pts) If 20 fermions with a mass of m are in the well, what is the mean energy of fermion at absolute temperature T=0 K? What is the Ferni energy of the system?

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