Fractional change in wavelength

[utkarshakash]

Homework Statement

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.

Homework Equations

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.

 

[haruspex]

What else might be conserved?

 

[utkarshakash]

What else might be conserved?

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?

 

[haruspex]

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?

That's what I would do.