1. Jan 9, 2009

monstersaurou

1. The problem statement, all variables and given/known data
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

2. Relevant equations

3. 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. Im pretty sure im missing out on something here. Any idea? Thanks!

2. Jan 9, 2009

Staff: Mentor

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.