Question

If the intensity of the incident light (whose frequency is greater than threshold frequency) is increased then explain its effect on (i) the maximum momentum that photoelectron could have and (ii) the minimum de -Broglie wavelength that photoelectron could have.

Answer 1

(i) Maximum K.E. of the emitted photo-electron of momentum `p_(max)` is given by
`K_(max)=(p_(max)^2)/(2m)=hv-phi_0`
`p_(max)=[2m(hv-phi_0)]^(1//2)`
Where `phi_0` is the work function of the metal surface used on which light falls. The above relation is independent of intensity of the incident light (i.e., number of photons falling per second per unit area of light)but depends on the frequency of the incident light.
If intensity of the incident light is increased without charging its frequency, the maximum momentum of the emitted photoelectrons remains unchanged.
(ii) The minimum de-Broglie wavelength of the emitted photoelectron of maximum momentum
`p_(max)` is, `lambda_(min)=h/(p_(max))`
It is alos independent of intensity of incident light. Thus, minimum de-Broglie wavelength of emitted photoelectron remains unchanged with the increase in intesity of the incident light.