AS Daily A Level Physics question
In a vacuum photocell, a clean caesium-coated cathode has a threshold wavelength of 600 nm. With 400 nm light at low intensity, the stopping potential needed to just reduce the photocurrent to zero is measured as 0.70 V, with the collector made negative relative to the cathode. The same apparatus is then used with 300 nm light of the same low intensity. Which statement must be true? (Use proportional reasoning rather than quoting equations.)
Answer
The correct answer is A.
Correct: A — About 1.4 V with the same (collector negative) polarity; doubling the intensity leaves this value unchanged. A is correct because photon energy varies inversely with wavelength and the threshold provides the fixed work-function offset, so the stopping potential scales with (1/λ − 1/λ0); from 400 nm to 300 nm this factor doubles, so 0.70 V becomes about 1.4 V, and intensity changes rate of emission, not the maximum electron energy or the required (retarding) polarity. B suggests reversing the polarity; more energetic electrons require a larger magnitude of the same retarding polarity (collector negative), not the opposite. C treats the dependence as proportional to wavelength (rather than to 1/λ with a threshold offset) and assumes intensity alters electron energy; intensity affects current, not the stopping potential. D confuses the threshold condition: wavelengths shorter than the threshold (300 nm < 600 nm) do eject electrons, while increasing intensity cannot overcome a below-threshold photon energy.