# Recoil energy

1. Jan 22, 2008

### cks

[SOLVED] recoil energy

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

Calculate the recoil energy and velocity of a hydrogen atom in a transition from
the state « = 4 to the state AT = 1, in which a photon is emitted.

2. Relevant equations

E=-13.5/n^2

E=mc^2/sqrt(1-v^2/c^2)

3. The attempt at a solution

|E4-E1|=13.6-13.6/16 eV = 12.75 eV

Invoking the total energy,

Before emission
mc^2 = E recoil + |E4-E1|=> E recoil = 1.50 *10^-10 J

I couldn't get the correct answer. I wonder what is wrong? am I understanding the meaning of recoil energy wrongly?

2. Jan 22, 2008

### Shooting Star

Recoil energy only pertains to the KE, and should not include the rest energy.

3. Jan 26, 2008

### cks

Thank you, I finally got it.

4. Feb 1, 2008

### cks

$${\frac {-1/4\,i}{w}}$$

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