Arthur H. Compton published his light photon scattering theory in 1922. He derived a remarkably elegant formula which now bears his name, the Compton scattering formula: λ' - λ = λ_c(1 - cos(φ). It was derived basically from energy and momentum conservation considerations for collision of x-ray or gamma-ray photons with electrons within the atoms of light elements. Due possibly to the sterling reputation of Compton as a physicist, his theory was readily accepted. But there is a critical flaw in the derivation of the Compton formula that should render the formula dubious. In the derivation, Compton assumed the scattering electron to be initially at rest. The original experiment of Compton used carbon graphite as the scattering target. The ionization energy of carbon is about 11.3eV and this is also the kinetic energy of the least bound electrons in the carbon atom. For the scattering angle of 10°, the energy lost to the x-ray photon which ended up as the recoil energy of the scattered electron was around 9.04eV. This shows that the initial kinetic energy of the scattering electron is not insignificant and should not be ignored. This unjustified assumption in the derivation makes the generality of the Compton scattering formula now dubious.