if every metal has a definite work function then why don't photoelectrons eject with same kinetic energy if the incident radiation is monochromatic and has a fixed energy?

Work function of a metal is the minimum energy required by an electron to just escape from the metal surface with zero velocity , so as to overcome the restraining force at the surface.

Every metal has a definite work function(φ_o) , eg: Work function of caesium is 2.14 eV, platinum is 5.65 eV etc.

When a monochromatic light having photon frequency  ν is incident  on a photosensitive metal surface. The energy of the photon(hν) is spent in:

1. A part of the energy of photon is used in liberating the electrons from the metal surface which is equal to the  work function φ_o of the metal.

2. The rest of the energy is used in imparting the maximum kinetic energy K_max to the emitted photo electron.

 

i.e. we can say thay Energy of incident radiation, 

So the kinetic energy of the emitted photo electron depend on the work fuction of the metal from which the electrons are emitted.Work fuction is different for different metals. Hence the photoelectrons ejected will not have same kinetic energy.