The photoelectrons  emitted from  a metal  surface are such that their  velocity

Suppose radiation of energy E+ϕ is incident on a metal surface. ϕ is the work function and is the energy need to eject a photoelectron..Assume all of E gets converted to Kinetic energy. There would be molecules that absorb energy lying from 0 to E.
And hence their velocities would lie between 0 and v.