HKU PHYS2265 Test1复习(论述)

• 瑞利-金斯定律(Rayleigh-Jeans Law)：

• 维恩位移律 (Wien's Displacement Law)：

• 斯特藩-玻尔兹曼定律 (Stefan-Boltzmann Law)：

• 普朗克假说 ：

1, (Conceptual Questions 2 Q3) Consider the following characteristics of the photoelectric effect. Which of these cannot be explained by classical physics? （答案由Gemini整理）

(i) The generation of photoelectrons.

Yes. Classical wave theory predicts that the electric field of an incoming light wave exerts a force on electrons in the metal, doing work and transferring energy until electrons gain enough kinetic energy to escape.

(ii) The existence of a threshold frequency.

No. Classical physics assumes light energy depends solely on light intensity, not frequency. It predicts that light of any frequency should eventually eject electrons if the intensity is high enough or given enough time. However, experiments show no electrons are emitted below a specific threshold frequency, regardless of intensity.

(iii) The photoelectric current increases with increasing light intensity.

Yes. Classical theory holds that higher light intensity means a greater rate of energy transfer, which frees more electrons per unit time and thus produces a larger photoelectric current.

(iv) The photoelectric current is independent of the anode-cathode potential difference ΔV for ΔV > 0.

Yes. Once the positive accelerating potential ΔV is large enough, all photoelectrons emitted per second are collected by the anode. The current reaches saturation and cannot increase further with higher potential. 

(v) The photoelectric current decreases slowly as ΔV becomes much more negative.

Yes.A negative potential creates a retarding electric field that opposes the motion of electrons. Because emitted electrons possess different initial velocities and directions, fewer electrons have enough kinetic energy to reach the anode as the potential becomes increasingly negative, resulting in a gradual decrease in current.

(vi) The stopping potential is independent of the light intensity.

No. Classical theory predicts that higher light intensity supplies more energy per electron, which should increase the maximum initial kinetic energy and require a larger stopping potential. Experimentally, stopping potential depends only on light frequency, not on intensity.

(vii) The photoelectric current appears almost instantly when the light is turned on.

No. In classical wave theory, at very low light intensity, the energy rate received by an individual electron is extremely small, predicting a long time lag (hours or days) for the electron to accumulate enough energy to escape. Experimentally, photoelectrons are emitted almost instantaneously.

2, (Conceptual Questions 2 Q3)

3, (2016/17 Test 1 - Q1(a)) Explain why incorrect: "When shining radio wave on a block of sodium metal, photo-electrons come out only after about a few seconds."（答案由Gemini整理）

Radio wave frequencies are below the work function cutoff frequency of sodium, so no photoelectrons can be emitted regardless of time; if above cutoff, emission is instantaneous.

4, (2017/18 Test 1 - Q1(a)) State using no more than four sentences the implications of Photoelectric effect.

The maximum k.e. of emitted electrons is independent of light intensity (1), the existence of a cutoff frequency of light below which no photo-electron is found (2), and instantaneous emission of photo-electrons when the light is turned on (3) all point to the particle nature of light, which classical wave theory cannot explain.

• 短波极限仅取决于加速电压 V，与粒子质量无关。

• 双峰成因：移动峰（Shifted peak）来自于光子与近乎自由的碰撞电子散射；未移动峰（Unshifted peak）来自于光子与束缚极紧的原子/整个原子散射，因为原子质量极大，波长偏移几乎为零。
  
• 适用范围：康普顿波长偏移最大约为 0.00485 nm (ceta取180°，2h/(m_e·c))。对于可见光、无线电波或电视信号，这一偏移量相对其本身波长微不足道。

1, (Conceptual Questions 2 Q9) An isolated atom can emit a photon and the atom’s internal energy drops. This process is called spontaneous emission. Can an isolated electron emit a photon? Why or why not?

No. This is the reverse of a completely inelastic collision. Kinetic energy would have to increase, meaning that internal energy would have to decrease. The photon has zero internal energy, and the electron’s internal energy cannot be changed as it is a fundamental particle.

1, (2024/25 Test 1 - Q1(II)) True or False: The production of X rays by the bremsstrahlung process can be regarded as an inverse photoelectric effect.

True. According to the photon theory, an X-ray photon is produced in the

bremsstrahlung process (by the bombardment of electrons on a target) due to part of kinetic energy of incoming electrons is converted into photon energy. So this process is equivalent to an inverse photoelectric effect in which the energy of the incident photon is delivered to the metal to release an electron from the metal.

2, (2024/25 Test 1 - Q3(a)) Explain why two peaks would be observed in the spectrum of scattered X-ray photons for Compton scattering at any angle θ ≠ 0 ?

(图片来自 Chapter 2 Lecture note）

For Compton scattering at any angle θ ≠ 0 , two peaks would be observed in the spectrum of scattered X-ray photons: one is near the wavelength of the incident X-ray photons and the other is at a longer wavelength. 

The shifted peak is due to Compton scattering of X-ray photons by the nearly free electrons in the target while the unshifted peak is due to Compton scattering of X-ray photons by the tightly bound electrons in the target. For the latter case, the whole atom recoils from the X-ray photon which results in a nearly zero wavelength shift of the photon.

• 重原子核的作用：维持动量守恒，吸收的能量可忽略不计。

• 德布罗意波长 (de Broglie Wavelength)：λ = h/p

位置-动量不确定性：被限制在微观尺寸r内的粒子（如原子核内的中子、势阱中的粒子），位置不确定度 ▲x ≈ r，导致必有最小动量不确定度

，因此最低动能不能为 0（基态能量不为零）。且空间受限越小（r越小），最低能量越高。

1, (2017/18 Test 1 - Q2(a))

Δx = 0 implies Δp is infinite by the Heisenberg uncertainty principle. Hence, the particle cannot be at rest.

2, (2023/24 Test 1 - Q1(V)) True or False: If lifetime of an excited atom increases, the minimum fractional uncertainty（相对不确定度） of the emitted photon's wavelength increases.

思路：先用海森堡不确定性原理（能量-时间）推出能量不确定度，再将能量不确定度与波长不确定度联系起来（找到能量和波长的关系式后求导）。

3, (2024/25 Test 1 - Q1(IV)) True or False: A neutron trapped within an atom has a non-zero minimum energy which increases as radius r increases.

1, (2016/17 Test 1 - Q1(e)) Explain why incorrect: 

（答案由Gemini整理）