Questions: Work Function and Photoelectric Energy Analysis

Question 1

A physicist shines light of frequency f = 0.8f₀ on a metal, where f₀ is the threshold frequency. The light intensity is extremely high — 1000 times the intensity used in previous experiments. What happens?

• A. Electrons are emitted with low kinetic energy, since some intensity can compensate for insufficient frequency
• B. No electrons are emitted, regardless of intensity, because each photon carries insufficient energy to overcome the work function
• C. Electrons are emitted after a brief time delay while energy builds up from many photons
• D. Electrons are emitted with kinetic energy proportional to the intensity

Answer: (B)

Each photon interacts with a single electron in an all-or-nothing transaction. A photon of frequency f carries energy hf; if hf < W (the work function), no individual photon can free an electron regardless of how many photons arrive. Intensity determines how many photons per second hit the surface — it increases the number of available transactions, but each transaction still involves only one photon of the same energy. There is no mechanism by which multiple low-energy photons pool their energy to free one electron (at least not at these intensities). This is precisely the result that refuted the classical wave theory.

Question 2

A researcher doubles the intensity of light shining on a metal above its threshold frequency. What changes?

• A. The maximum kinetic energy of emitted electrons doubles
• B. The threshold frequency decreases
• C. The photocurrent (number of electrons emitted per second) roughly doubles, but the maximum kinetic energy is unchanged
• D. Both the photocurrent and the maximum kinetic energy increase proportionally

Answer: (C)

Intensity determines how many photons per second arrive at the surface, which determines how many electrons are freed per second — the photocurrent. But the energy each electron receives comes from a single photon (energy = hf), and the maximum kinetic energy is KE_max = hf − W. Doubling the intensity doubles the number of photons (and thus electrons) but does not change the energy per photon. Therefore KE_max is unchanged. Only changing the frequency of the light changes KE_max. This separation — intensity controls count, frequency controls energy — is the signature of light quantization.

Question 3

The maximum kinetic energy of photoelectrons depends on the frequency of the incident light but not on its intensity.

• T. True
• F. False

Answer: True

KE_max = hf − W. The work function W is a fixed property of the metal; the photon energy hf depends only on frequency f. Intensity tells you how many photons per second arrive, which sets the photocurrent, but each electron's maximum kinetic energy is set by a single photon interaction. No matter how many photons arrive, each electron can receive at most one photon's worth of energy (hf), so the maximum is determined solely by frequency. This is one of the clearest experimental signatures distinguishing the photon picture from the classical wave picture.

Question 4

The classical wave theory of light predicts that increasing light intensity should eventually cause photoelectron emission even below the threshold frequency, given enough time for energy to accumulate.

• T. True
• F. False

Answer: True

This is correct — and it is precisely what the classical wave theory predicted that turned out to be wrong. Classical wave theory treated light as a continuous wave delivering energy uniformly across the metal surface. Given enough time (or enough intensity), any surface electron should accumulate enough energy to escape, regardless of frequency. Experiments found the opposite: below the threshold frequency, no electrons are ever emitted no matter how long you wait or how bright the light is. This is the result that proved the classical picture was wrong and required Einstein's photon hypothesis.

Question 5

Explain why Einstein's photoelectric equation KE_max = hf − W requires the photon hypothesis, and what observation it accounts for that the classical wave theory cannot explain.

Model answer: The equation assumes light comes in discrete packets (photons) each carrying energy hf, and that one photon interacts with one electron. The work function W is the minimum escape energy; whatever energy remains after paying this cost becomes kinetic energy, giving KE_max = hf − W. The classical wave theory cannot explain why there is a sharp threshold frequency below which no emission ever occurs regardless of intensity, nor why KE_max depends on frequency rather than intensity. Both observations follow naturally if light is quantized: a photon below threshold simply lacks the energy to free an electron, no matter how many arrive.

The stopping potential experiment (measuring V₀ vs. f) provides a direct, quantitative test: the linear relationship V₀ = (h/e)f − W/e gives Planck's constant as the slope. Millikan's precise measurements confirmed Einstein's equation and reluctantly validated the photon hypothesis. The conceptual point — that 'how many photons' and 'how much energy per photon' are independent quantities controlled by intensity and frequency respectively — remains one of the cleanest illustrations of quantization in introductory physics.