Is the photon scattering elastically?

[leonmate]

Homework Statement

Photons and electrons interact via Compton scattering. If the photon scattering angle is θ=30, compute the relative change in wavelength for photons of wavelength λ=10^-2 m.
Is the photon scattering elastically? (The electron Compton wavelength is: λ_c=2.4x10^-12m)I've solved this problem as so:

Δλ = λ_c(1-cosθ) = 3.22x10^-13

So the relative change in wavelength:

Δλ / λ = 0.322

I believe this isn't elastic scattering but I don't really understand why. Any help would be appreciated.

 

[TSny]

Homework Statement

Photons and electrons interact via Compton scattering. If the photon scattering angle is θ=30, compute the relative change in wavelength for photons of wavelength λ=10^-2 m.

Is there a typo in the exponent for λ?

I've solved this problem as so:

Δλ = λ_c(1-cosθ) = 3.22x10^-13

So the relative change in wavelength:

Δλ / λ = 0.322

Looks correct if the initial wavelength is 10^-12 m.

Is the photon scattering elastically?
I believe this isn't elastic scattering but I don't really understand why. Any help would be appreciated.

See http://en.wikipedia.org/wiki/Inelastic_scattering

 

[leonmate]

Yes, supposed to be 10^-12

I've read through that, and some other stuff. Am i right in saying: A collision is elastic if the re-emitted wave has the same frequency as the incident wave?

Thus, as there has been a change in wavelength, there must have also been a change in frequency so the collision in the question is inelastic?

 

[TSny]

Yes, that's right. Energy of a photon depends only on wavelength (or frequency). So, if the wavelength of the photon changes then the energy of the photon changes. If the energy of the scattered particle changes, then the scattering is inelastic.

 

[orsanyuksek2013]

E_photon = h ƒ = h c / λ

where

h: The Planck´s constant
f: The frequency of the photon
c: The speed of light in vacuum
λ: The wavelength of the photon

Because of the decrease in the wavelength of the photon, the energy of the photon decreases. Some of this energy is transferred to the electron and some is lost during the scattering process. Because the energy of the whole system decreases (energy of the photon + energy of the electron), the Compton scattering is inelastic.

 

[TSny]

Because of the decrease in the wavelength of the photon, the energy of the photon decreases. Some of this energy is transferred to the electron and some is lost during the scattering process. Because the energy of the whole system decreases (energy of the photon + energy of the electron), the Compton scattering is inelastic.

In the normal treatment of Compton scattering, the total energy of the electron-photon system remains constant. That's one of the assumptions that go into deriving the Compton scattering formula. So, no energy is lost in the scattering process. (Unless you want to take into account the binding energy of the electron in its host atom. But this is a vary small energy compared to the energy of the x-ray photons used in a typical Compton scattering process.)

When the total kinetic energy of a collision is conserved, then the collision is elastic. Nevertheless, the scattering can still be inelastic (as in Compton scattering). That is, elastic collision does not imply elastic scattering. It's certainly confusing.

See http://en.wikipedia.org/wiki/Inelastic_scattering and http://en.wikipedia.org/wiki/Compton_scattering