Questions: Photons as Particles with Energy and Momentum

Question 1

A metal surface is illuminated by dim violet light and ejects electrons. The same surface is then illuminated by very bright red light and ejects no electrons at all. Why?

• A. Violet light is more intense, delivering more total power to the surface
• B. Red light has a higher frequency than violet light, requiring photons to carry more energy
• C. Each violet photon carries enough energy (E = hf) to overcome the work function, while each red photon does not — regardless of how many red photons arrive per second
• D. Dim light produces a smaller electric field, and electric fields drive electron emission

Answer: (C)

This is exactly the photoelectric puzzle that classical wave theory cannot explain. In classical physics, increasing intensity should eventually deliver enough energy to eject electrons — but it doesn't. The photon model explains why: each photon carries energy E = hf, and ejection requires a single photon to deliver at least φ (the work function) all at once. High-intensity red light sends many low-energy photons; none has enough energy individually. Dim violet light sends few high-energy photons; each one can eject an electron. Intensity controls the rate of ejection (how many per second), but frequency controls whether any ejection occurs at all.

Question 2

Compared to classical electromagnetic wave theory, what specific feature of the photoelectric effect does the photon model uniquely explain?

• A. Why light travels at a fixed speed c in vacuum
• B. Why the maximum kinetic energy of ejected electrons depends on the frequency of light, not its intensity
• C. Why light exhibits interference and diffraction patterns when passing through slits
• D. Why electromagnetic waves carry both electric and magnetic field components

Answer: (B)

Classical wave theory predicts that increasing intensity (amplitude) should increase the energy delivered to electrons, eventually allowing ejection regardless of frequency. Experiments showed instead that maximum kinetic energy scales with frequency (KE_max = hf − φ) and is completely independent of intensity. No intensity of red light, however bright, exceeds the threshold. This sharp frequency dependence is inexplicable with continuous waves but follows immediately from E = hf: per-photon energy is set by frequency, not by how many photons arrive. Interference and diffraction (option C) are wave behaviors that the photon model supplements rather than replaces.

Question 3

Increasing the intensity of a light beam increases the energy carried by each individual photon.

• T. True
• F. False

Answer: False

Intensity measures the number of photons arriving per unit area per unit time (photon flux), not the energy of each photon. Per-photon energy is fixed by E = hf — determined entirely by frequency. Doubling the intensity doubles the photon count rate, which doubles the rate of electron ejection (if above threshold), but leaves each photon's energy unchanged. This is the central quantum insight that breaks with classical wave intuition: energy comes in discrete packets whose size is set by frequency, not amplitude.

Question 4

Although photons have zero rest mass, they carry real, measurable momentum that can be transferred to matter in collisions.

• T. True
• F. False

Answer: True

Photon momentum p = E/c = h/λ is not hypothetical — it was directly confirmed by the Compton effect (1923). X-ray photons scattered off electrons emerged with longer wavelengths (lower energy), and the electrons recoiled with precisely the momentum transferred by the photons, consistent with relativistic particle mechanics applied to a zero-rest-mass particle. The wavelength shift Δλ = (h/m_ec)(1 − cos θ) depends on scattering angle, exactly as predicted. Photons carry momentum without having rest mass because they always travel at c — they exist only in motion.

Question 5

Why does the equation E = hf represent a conceptual revolution, and what two previously incompatible frameworks does it bridge?

Model answer: E = hf bridges the wave description of light (characterized by frequency f, a property that only makes sense for a wave) and the particle description (characterized by discrete energy E, a property that belongs to a localized quantum). Before quantum mechanics, these frameworks were considered mutually exclusive — something was either a wave or a particle. E = hf shows they describe the same physical object from complementary angles, with Planck's constant h as the conversion factor between them. A photon propagates as a wave (producing interference) but interacts as a particle (depositing E = hf in a single collision). This wave-particle duality extended to matter through de Broglie's λ = h/p.

The revolution is not just mathematical but ontological: it requires abandoning the classical demand that an object be one kind of thing. Photons are neither classical waves nor classical particles — they are a new category that inherits features of both depending on the experimental context. E = hf is the hinge between the two descriptions, and the appearance of the same constant h in both the photon energy formula and the de Broglie matter-wave relation (λ = h/p) reveals that this duality is not a quirk of light but a universal feature of quantum objects.