I am reading some material about compton effect. I am wondering in what reason we have to use short wavelength photon in compton scattering, why can't we use long wavelength instead?
The usual Compton scattering equations and their derivation assume the electron is "free." But in reality the electrons we have to work with are usually bound in atoms. If photon energy is a lot more than the electron binding energy, then we can consider the electron "free" as a good approximation. For example, if the photon has a few tens or hundreds of keV (X-rays or gamma rays respectively), versus the typical binding energy of a few eV.
I would also add that for longer wavelenghts, for example in the visible range, the effect is negligible because delta lambda would be much smaller than lambda itself.