Questions: Stopping Potential and Maximum Kinetic Energy

Question 1

A physicist doubles the intensity of monochromatic light hitting a metal surface while keeping the frequency constant. What happens to the stopping potential?

• A. It doubles, because twice the energy is hitting the surface per second
• B. It increases, but by less than a factor of two, due to electron-electron interactions
• C. It remains unchanged, because stopping potential depends only on photon frequency, not intensity
• D. It decreases, because more electrons compete for the available energy

Answer: (C)

This is the central experimental fingerprint of quantization. Stopping potential measures KE_max = hf − W, which depends only on the frequency of the photons and the work function of the metal. Doubling intensity means twice as many photons per second — so twice as many electrons are ejected (higher photocurrent) — but each photon still carries energy hf, so each emitted electron still has the same maximum kinetic energy. The stopping potential is unchanged. A classical wave model would predict that higher intensity means higher amplitude and thus more energy delivered to each electron — precisely what the experiments refuted.

Question 2

A plot of stopping potential V_s versus light frequency f for a metal produces a straight line. The slope of this line equals:

• A. The work function W of the metal
• B. The threshold frequency f₀ below which no electrons are emitted
• C. h/e — Planck's constant divided by the elementary charge
• D. e/h — the elementary charge divided by Planck's constant

Answer: (C)

Rearranging eV_s = hf − W gives V_s = (h/e)f − W/e. This is a linear equation in f with slope h/e and y-intercept −W/e. Since the electron charge e is independently known (from Millikan's oil-drop experiment), measuring the slope of this line gives a direct experimental determination of Planck's constant h. This is historically significant: Millikan's careful measurements of this slope confirmed Einstein's quantum hypothesis and provided one of the first precise values of h.

Question 3

The y-intercept of a V_s versus frequency plot is negative, equal to −W/e, where W is the work function of the metal.

• T. True
• F. False

Answer: True

From V_s = (h/e)f − W/e, the y-intercept (the value of V_s when f = 0) is −W/e, which is negative since W > 0. This is physically consistent: at zero frequency there are no photons with enough energy to eject electrons, and the intercept simply reflects the threshold energy barrier. The x-intercept (where V_s = 0) corresponds to f₀ = W/h, the threshold frequency below which no photoemission occurs.

Question 4

Increasing the intensity of monochromatic light increases the maximum kinetic energy of emitted photoelectrons, because a higher-amplitude wave delivers more energy to each electron at the surface.

• T. True
• F. False

Answer: False

This is precisely what classical wave theory predicted — and precisely what experiments disproved. In the quantum picture, light consists of photons each carrying energy hf regardless of intensity. Increasing intensity means more photons per second, so more electrons are ejected (higher photocurrent), but each individual photon-electron interaction delivers the same energy hf. KE_max = hf − W is intensity-independent. The classical wave prediction (more intensity → more energy per electron) was falsified by the fact that V_s doesn't change with intensity.

Question 5

Why does the experimental relationship between stopping potential and light frequency provide direct evidence for the quantization of light?

Model answer: If light were a classical continuous wave, its energy would scale with intensity (amplitude squared), so higher-intensity light should eject electrons with greater maximum kinetic energy — the stopping potential would depend on intensity. Instead, experiments show that V_s depends linearly on frequency and is completely unaffected by intensity. This can only be explained if light delivers energy in discrete packets (photons) of fixed size hf: each photon-electron interaction transfers exactly hf regardless of how many photons arrive per second. The linear V_s vs. f plot with slope h/e is the direct experimental signature of this quantization.

This is historically one of the cleanest experimental demonstrations that energy quantization is not a mathematical convenience but a physical fact. Millikan set out to disprove Einstein's photon hypothesis and ended up confirming it precisely. The prediction of a linear relationship with slope h/e — and its verification — was a major step in establishing quantum mechanics.