Solving for the speed of a recoiling H atom

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silex
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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
 
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Using conservation of momentum solved the problem, thanks.