A metal has a definite work function. Why do photo-electrons not come out all with the same energy even if irradiated with monochromatic light?

Electrons in a metal do not have the same energy. According to band theory, electrons of a metal occupy closely placed (near continuous) energy levels in the conduction band. The energy level for which the probability of occupancy is 50% is an important level (known as the Fermi level) and the energy required to lift an electron from this level is known as work function. Since all electrons in the metal do not belong to this level but they occupy near-continuous bands of levels, therefore, for a given incident radiation, the electrons knocked from different levels come out with different energies.