# Energy of scattered photon

1. May 18, 2006

### Reshma

An electron of mass 'm' and speed 'v' collides with a gamma ray photon of initial energy hf0, as measured from the laboratory frame. The photon is scattered in the electron's direction of travel. Verify that the energy of the scattered photon, as measured in the laboratory frame, is:
$$E = hf_0\left(1 + \frac{2hf_0}{mc^2}\sqrt{\frac{1 + v/c}{1 - v/c}}\right)^{-1}$$

Well this also seems to be a Compton effect problem. The relativistic Doppler equation for frequency is given by:
$$f = f_0\sqrt{\frac{1 - \beta}{1 + \beta}}$$
where $\beta = v/c$

Need guidance to apply this formula to obtain above result....

2. May 18, 2006

### Andrew Mason

Use the Compton formuala to determine the energy of the photon after the collision in the frame of the electron before the collision. Then apply the Doppler equation to get the energy in the lab frame.

AM

Last edited: May 18, 2006
3. May 26, 2011

### BlazzedTroll

Thank you for the hints here on how to solve it but I have been working on this problem for several days now and I keep getting to similar places after using the compton scattering and doppler effect but I cant see how sqrt((1-v/c)/1+v/c)) is becoming sqrt((1+v/c)/(1-v/c))
can someone plz explain this?

4. May 26, 2011

### Andrew Mason

v is negative if the observer is moving away from the source and positive if the observer is moving toward the source.

AM