# Hydrogen atom emitting a photon

1. Apr 9, 2014

### STJ

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

Consider the following.
(a) For a hydrogen atom making a transition from the n = 4 state to the n = 3 state, determine the wavelength of the photon created in the process. (Already solved this, 1.86x10^3 nm)

(b) Assuming that the atom was initially at rest, determine the recoil speed of the hydrogen atom when it emits this photon.

2. Relevant equations

λ=hc/ΔE

3. The attempt at a solution

I've done one like this previously, but we were given the energy of the photon colliding with the atom. Found the Kinetic Energy, set it equal to 1/2mv^2 and solved for v. I don't think I can do this for part b. I think this has something to do with momentum perhaps? I'm kind of lost on this one.

2. Apr 9, 2014

### patrickmoloney

Momentum of photon = $\frac{h}{ \lambda}$

Conservation of momentum says that this momentum must be in the opposite direction of the hydrogen atom.

$p = \frac{h}{\lambda} = \frac{6.63*10^{-34}}{1.83*10^{-6}} = 3.62*10^{-28} kg \cdot ms^{-1}$

$V_{H-atom} = \frac{p}{m} = \frac{3.62*10^{-28}}{1.67*10^{-27}} = 0.22 ms^{-1}$