At early 1920 when the particle nature of photon suggested by the photoelectric effect was still being debated, the Compton Effect gave clear and independent evidence of particle-like behavior. The Compton hypothesis is suggested that when an X-ray photon is scattered it spends all of its energy and momentum upon some particular electron (which is treated as being at rest). This electron in turn scatters the ray in some definite direction. The change in momentum of the X-ray photon due to the change in its direction of propagation results in a recoil of the scattering electron. The energy in the scattered photon is thus less than the energy of the incident photon by the kinetic energy of recoil of the scattering electron. The corresponding increase in the wavelength of the scattered... photon is (λf − λi) = (h/m0C) × (1− cosθ) and the time it takes for the incident photon to change its wavelength is t = (h/m0C2) × (1− cosθ), where h is the Planck’s constant, m0 is the rest mass of the scattering electron, C is the speed of light in vacuum, and θ is the angle between the incident and the scattered photon. Experimental result is given which show that for graphite and the Mo- Kα radiation the value of t (for θ =90o) has been found to be 7.333 × 10 −21 s which being satisfactorily close to the computed value (8.089 × 10 −21 s). In the case of θ =135o, the value of t has been found to be 0.133 × 10 −19 s which also being satisfactorily close to the computed value (0.138 × 10 −19 s). However, the value of t has been found to vary with θ in agreement with the theory, increasing from 7.333 × 10 −21 s (θ =90o) to 0.133 × 10 −19 s (θ =135o). Velocities of recoil of the scattering electrons have not been experimentally determined. This is probably because the electrons which recoil in the process of the scattering of X-rays have not been observed. However, velocity of recoil of the scattering electron (when θ =90o) has been calculated using: (1) Law of Conservation of Energy. (2) Law of Conservation of Momentum. The value of v computed using the Law of Conservation of Energy was found to be 0. And the value of v computed using the Law of Conservation of Momentum was found to be 0.04C. Using the conservation laws the law of variation of mass with velocity has been derived which in bad agreement with the Einstein’s law of variation of mass with velocity. But according to which also when v → C, mE→ ∞.i.e., an electron travelling at the speed of light would have infinite mass and hence, no material particle can have a velocity equal to the speed of light in vacuum.