AS Daily A Level Physics question
In a lab, monochromatic light of wavelength 400 nm is shone onto a clean metal, giving a stopping potential of 0.90 V. The intensity is kept the same but the wavelength is reduced by 10% to 360 nm. Which statement must be true about the new stopping potential? (Take hc ≈ 1240 eV·nm.)
Answer
The correct answer is C.
Correct: C — It rises to about 1.24 V (≈38% increase), because photon energy increases while the work function is unchanged. A 1/λ increases by 11%, but stopping potential depends on (photon energy − work function), so subtracting the fixed work function means the percentage rise in Vs is larger than 11%. B Stopping potential depends on photon energy, not on intensity; keeping intensity the same does not keep Vs the same when wavelength changes. C Using 1240/λ gives E(400 nm) ≈ 3.10 eV so Φ ≈ 3.10 − 0.90 = 2.20 eV; at 360 nm, E ≈ 3.44 eV so Vs ≈ 3.44 − 2.20 = 1.24 V, about a 38% increase. D Fewer photons per second at the same intensity is true for shorter wavelength, but Vs is set by maximum electron energy, not by photon arrival rate, so it does not decrease.