1. The problem statement, all variables and given/known data Why is it that even for incident radiation that is monochromatic,photoelectrons are emitted with a spread of velocities? 2. Relevant equations 3. The attempt at a solution Possibly, the incident radiation is partly used up in increasing the thermal energy of the crystal...Now,we claim that all the energy of the absorbed photon is given to an emitted electron.Here we are neglecting the energy taken up by the lattice. I think,for photoelectric effect it is possible to have KE(max)=h(nu)-(phi) when we neglect the energy taken up by the lattice.If we neglect the energy exciting the lattice,we must replace KE(max) by KE. This also explains why the photoelectric measurements are very sensitive to the nature of emitting surface.If it is a conductor,standard photoelectric current is obtained---here the energy is totally used up emitting electrons(I do not know if for suitable conductors,the velocity spread is observed);for non-conductors,current falls to drastically low values.Here,the energy is converted to heat... Please check.