Help Christoph: Solve the Photon Scattering Problem

[Khasimir]

Hallo

I don't understand why I can't use

Δλ = λ'- λ = h/(m·c) · ( 1 - cos φ )
and ΔE = h · c / Δλ

for getting the energy ΔE which is transferred to the electron

In school we did it like this: 1/f'- 1/f = h/(m·c) · ( 1 - cos φ )
<-> E' = hf' = hf/(1 + hf(1 - cos φ )/(mc^2))

-> ΔE = E (energy of photon before scattering) - E' (energy of photon after)

I really need help

Christoph

 

[jtbell]

$$\Delta E = E^\prime - E = \frac{hc}{\lambda^\prime} - \frac{hc}{\lambda} = hc \left( \frac{1}{\lambda^\prime} - \frac{1}{\lambda} \right)$$

This does not equal $hc / \Delta \lambda$ because

$$\frac{1}{\lambda^\prime} - \frac{1}{\lambda} \ne \frac{1}{\lambda^\prime - \lambda}$$