Solving for the speed of a recoiling H atom

[silex]

Hey everyone,
I have a practice problem that I can't figure out:

A hydrogen atom is initially at rest and in the n=2 state. Subsequently, it decays to the ground state by emitting a photon. What is the speed of the recoiling atom afterwards? (Mass of H atom = 1.67 * 10^-27 kg)

My approach is to find the difference in energy between the two states by using E = -13.6/n^2 for each state (n=1 and n=2), then finding the energy difference, and setting that equal to (1/2)mv^2 and solving for v, but I'm not getting the right answer. (The correct answer is 3.4 m/s)
Can someone help me with this?

Thanks in advance

-s

 

[BornLogician79]

use 4 in work reverse?

 

[dav2008]

I would use conservation of momentum.

 

[silex]

Using conservation of momentum solved the problem, thanks.