Fractional change in wavelength

1. Dec 27, 2013

utkarshakash

1. The problem statement, all variables and given/known data
When a photon is emitted from an atom the atom recoils. The kinetic energy of recoil and the energy of photon come from the difference in energies between the states involved in the transition. Suppose a hydrogen atom changes its state from n=3 to n=2. Calculate the fractional change in wavelength of light emitted due to the recoil.

2. Relevant equations

3. The attempt at a solution

Difference in energies of states = -13.6(1/4 - 1/9)

This is equal to sum of KE of recoil and energy of photon(ΔE).

$\dfrac{mv^2}{2} + \delta E = -13.6 \left( 1/4 - 1/9 \right)$
From this I can find energy of photon released only if I know the velocity v.

2. Dec 27, 2013

haruspex

What else might be conserved?

3. Dec 28, 2013

utkarshakash

Momentum.
Using momentum conservation I can write

ΔE/c=mv.

Now if I plug v into energy conservation equation. I will get a quadratic in ΔE. Am I on the right track?

4. Dec 28, 2013

haruspex

That's what I would do.