Questions: The Photon Concept and Light as Quanta

Question 1

In a photoelectric effect experiment, red light illuminates a metal surface but no electrons are ejected. A student increases the brightness of the red light one hundredfold. What happens?

• A. Electrons are now ejected because the total energy striking the surface is much larger
• B. Electrons are still not ejected — each photon's energy is E = hf, determined by frequency alone, and red light photons are below the work function threshold regardless of intensity
• C. Electrons are ejected at a rate proportional to the brightness increase
• D. Multiple low-energy photons can combine to eject one electron once enough accumulate

Answer: (B)

This is the definitive test of the photon concept versus classical wave theory. Classical physics predicts that brighter light delivers more energy per unit area, so eventually enough energy should accumulate to eject electrons. But the photoelectric effect shows a sharp frequency threshold: below it, no electrons are emitted no matter how intense the light. Einstein's explanation: each electron absorbs exactly one photon, and a photon of red light simply doesn't have enough energy (E = hf) to overcome the work function. Increasing brightness means more photons, but each photon still carries the same energy. Only increasing frequency can raise individual photon energy above the threshold.

Question 2

A photon of ultraviolet light (frequency f₁) and a photon of red light (frequency f₂) both travel through vacuum. Which statement correctly compares their properties?

• A. Both travel at the same speed c, but the UV photon carries more energy (hf₁) and more momentum (h/λ₁)
• B. The UV photon travels faster because it carries more energy
• C. Both carry the same energy because energy depends on wave amplitude, not frequency
• D. The red photon has more momentum because its wavelength is longer

Answer: (A)

All photons travel at c in vacuum, regardless of frequency. Energy E = hf and momentum p = h/λ both increase with frequency (and decrease with wavelength). Since UV has higher frequency and shorter wavelength than red light, UV photons carry both more energy and more momentum. Option C confuses classical wave intensity (proportional to amplitude squared) with quantum energy — in the photon picture, amplitude relates to the number of photons, not individual photon energy. Option D inverts the momentum relation: shorter wavelength means larger p = h/λ.

Question 3

According to the photon model, a beam of light with higher intensity (brighter) contains more photons per second than a dimmer beam of the same frequency.

• T. True
• F. False

Answer: True

Intensity in the photon picture corresponds to the rate of photon arrival. Each photon still carries energy E = hf — fixed by frequency — but a brighter beam delivers more photons per unit time per unit area. This is why bright red light cannot eject electrons (each photon still lacks enough energy) but dim UV light can (each photon exceeds the work function). The distinction between 'more photons' and 'higher-energy photons' is the core of the photon concept.

Question 4

Planck introduced energy quantization (E = hf) as a genuine physical claim that light consists of discrete particles, a conclusion Einstein later confirmed with the photoelectric effect.

• T. True
• F. False

Answer: False

It was the other way around. Planck introduced quantization as a mathematical trick to fix the ultraviolet catastrophe — he did not initially claim light itself was composed of discrete particles. Einstein made the radical physical claim: photons are real particles, not a bookkeeping device. The photoelectric effect, which shows that energy transfer occurs in discrete quanta with a sharp frequency threshold, provided the experimental evidence for Einstein's particle claim. Planck was initially reluctant to accept the full physical implication of his own formula.

Question 5

Why does the sharp frequency threshold in the photoelectric effect disprove the classical wave theory of light, even when very intense (bright) light is used?

Model answer: Classical wave theory predicts that energy arrives continuously, so increasing brightness should always eventually eject electrons — given enough time, enough energy accumulates regardless of frequency. But experiments show that below a certain frequency threshold, no electrons are ejected no matter how bright the light or how long it shines. This is impossible if energy arrives continuously. The photon explanation resolves it: each electron must absorb a single photon, and the photon's energy E = hf depends entirely on frequency. If frequency is below the threshold, no individual photon has enough energy to overcome the work function, and 'accumulation' of multiple photon energies doesn't happen at the single-electron level.

The key failure of classical theory is the prediction that intensity should substitute for frequency at the threshold — that you could compensate for low-frequency light with higher brightness. The complete failure of this prediction, combined with the instantaneous ejection of electrons at any intensity above the threshold frequency, makes the continuous-wave model untenable. Einstein's photon hypothesis explains both features simultaneously: the threshold is about photon energy (frequency-dependent), and ejection is instantaneous because absorption is a single photon event.