Do all photoelectrons emitted from a metal surface possess th esame energy?

An electromagnetic wave of length lambda is incident on a photosensitive surface of negligible work function. If the photoelectrons emitted from the surface have the same de-Broglie wavelength lambda , prove that lambda=(2mc)/h lambda_1^2

Why do all electrons emitted during beta decay not have the same energy? give reasons.

If lamda_o and lamda be the threshold wavelength and wavelength of incident light , the velocity of photoelectron ejected from the metal surface is :

Why is that molecules of a liquid near the free surface possess extra energy?