Why Does Photon Energy Calculation Yield Different Results?

[monstersaurou]

Homework Statement

Find the momentum and energy of photons of light of wavelength 500nm. Usual data of h = 6.63 x 10^-34 and c = 3.0 x 10⁸ms^-1

Homework Equations

The Attempt at a Solution

> To get momentum, i simply take momentum = h/wavelength = 1.326 x 10^-27 kgms^-1

> To get energy I use E = hf = 3.96 x 10^-19 J

> However, i figured that an alternative way to get energy will be to use the equation p = mv. Since i have already calculated the momentum of my photon in the first step, and I know that the velocity of a photon is 3.0 x 10⁸ ms^-1, the mass of the photon will be 4.42 x 10^-36 kg. With this mass in mind, I can now use KE = 0.5mv² (m = 4.42 x 10^-36, v = 3.0 x 10⁸ ms^-1). Eventually, i obtain a KE of 1.99 x 10^-19 J.

> So there is now this paradox that E=hf gives me energy as 3.96 x 10^-19 J, while the alternative method gives me energy of 1.99 x 10^-19 J, which is half that of the former. I am pretty sure I am missing out on something here. Any idea? Thanks!

 

[Doc Al]

However, i figured that an alternative way to get energy will be to use the equation p = mv.

The equation p = mv only applies to particles moving slowly compared to light speed. It certainly doesn't apply to photons, which have m = 0.