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

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

 

[m2003]

,

I understand your confusion. While the equations you have mentioned are commonly used in photon scattering problems, it is important to understand the underlying principles and assumptions behind them.

The first equation, Δλ = λ' - λ = h/(m·c) · (1 - cos φ), is known as the Compton scattering formula. It is derived from the Compton effect, which describes the change in wavelength of a photon after it interacts with an electron. This formula assumes that the energy of the photon before and after scattering is the same, and only the wavelength changes due to the interaction with the electron.

However, in your school's approach, you have used the formula 1/f' - 1/f = h/(m·c) · (1 - cos φ), which is known as the energy conservation equation. This formula takes into account the change in energy of the photon after scattering, and it is based on the principle of energy conservation. This is why you have included the energy of the photon (E) in your calculation of ΔE.

Both equations are valid in different scenarios, and it is important to understand which one is appropriate for your specific problem. In general, the Compton scattering formula is used when the energy of the photon is much larger than the energy of the electron, while the energy conservation equation is used when the energy of the photon is comparable to or smaller than the energy of the electron.

I hope this helps clarify your confusion and provides a starting point for solving your photon scattering problem. It is always important to carefully consider the assumptions and principles behind the equations we use in science. Good luck with your research!