Question

Can we find the mass of a photon by the definition p = mv?

Answer 1

No, we cannot find the mass of a photon by the definition p = mv. The equation p = mv is valid only for objects that move with a velocity that is much slower than the speed of light. The momentum of a relativistic particle like photon is given by $pc=\sqrt{E^2-m^2{c}^4}$.
A photon has zero rest mass. Therefore, on putting m = 0 in the equation, we get
$p=\frac{E}{c}$, which is the valid equation for a photon.