(a) The figure shows the variation of photoelectric current measured in a photo-cell circuit as a function of the potential difference between the plates of the photo-cell when light beams A, B, C and D of different wavelengths are incident on the photo-cell. Examine the figure and answer: (i) Which light beam has the highest frequency and why? (ii) Which light beam has the longest wavelength and why? (iii) Which light beam ejects photoelectrons with maximum momentum and why?
Answer: (i) B (highest frequency), (ii) C (longest wavelength), (iii) B (maximum momentum).
Solution
The stopping potential (where each curve meets the potential axis on the retarding side) fixes the maximum kinetic energy, through eV0=hν−ϕ0. (i) **Highest frequency → beam B**: it has the greatest stopping potential, hence the largest Kmax and (for the same metal) the highest frequency. (ii) **Longest wavelength → beam C**: it has the smallest stopping potential, hence the lowest frequency and therefore the longest wavelength (λ=c/ν). (iii) **Maximum momentum → beam B**: the largest Kmax means the largest electron speed, and momentum p=mv=2mKmax is greatest for beam B.