# Compton scattering

#### Nyril

Hello,
I have a problem with demonstrating a relation in a Compton scattering exercise:
A low energy photon collides with an electron at rest. After the shock, the photon is backscattered.
It is supposed that the energy of the photon is very small compared with the energy of the electron at rest
I have to show that the ration between the energy of the backscattered photon and the kinetic energy acquired by the electron in a compton scattering is approximately c / v
where v is the speed of the electron
I use the energy conservation:
$$\displaystyle h\mu +m c^2=h\mu' +Ec +mc^2$$ and the relation $$\displaystyle \lambda'-\lambda=\frac{2h}{mc}$$
I have arrived on this $$\displaystyle \frac{E_\gamma}{Ec}=\frac{2h\mu c^2}{v^2(2h\mu+mc^2)}$$but there is no way i can obtain c/v...
Thank you so much for your help(Sorry for my english...)

#### Pmb

PHF Hall of Fame
Hello,
I have a problem with demonstrating a relation in a Compton scattering exercise:
A low energy photon collides with an electron at rest. After the shock, the photon is backscattered.
It is supposed that the energy of the photon is very small compared with the energy of the electron at rest
I have to show that the ration between the energy of the backscattered photon and the kinetic energy acquired by the electron in a compton scattering is approximately c / v
where v is the speed of the electron
I was bored so I looked at some old posts. In doing so it just occurred to me that this can't be correct since kinetic energy is expressed in terms of joules but c/v is unit less.

#### studiot

I was bored so I looked at some old posts. In doing so it just occurred to me that this can't be correct since kinetic energy is expressed in terms of joules but c/v is unit less.
Why not?

The ratio of photon energy to electron kinetic energy is also dimensionless is it not?

However I am concerned with the OP statement that the energy of any object at rest (ie the electron) is large compared with the input energy to the system (ie the photon)

OP after you have tidied up your statement of the problem, think about conservation of momentum to provide a velocity for the electron, subsequent to the impact.

This will give you an expression to calculate the energy of the electron.

Then remember that the velocity of the backscattered photon is -c, because it is backscattered.

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#### Pmb

PHF Hall of Fame
Probably because I made a boo boo.

That's one of the problems that arises from poor concentration.