Compton Scattering MCQ: Min No. of Collisions to Absorb Photon

[neelakash]

Homework Statement

A photon of wavelength $$\lambda$$ enters an electron gas.What is the minimum number of collisions that could result in the photon being completely absorbed in the gas?

(a) $$\approx$$$$\lambda$$$$\frac{mc}{2h}$$

(b) $$\approx$$$$\lambda$$$$\frac{mc}{h}$$

(c) $$\approx$$$$\lambda$$$$\frac{2mc}{h}$$

Homework Equations

The Attempt at a Solution

I have done in following way:

It can be shown that for compton scattering,

$$\frac{ E }{ \Delta E }$$=$$\frac{mc^2}{ h\nu\[1-cos\phi]}$$

where $$\large E$$ is the initial energy of the photon and $$\Delta E$$ is the energy lost per scattering phenomenon.

Now,demanding for the minimum number of collision,I had (a) the correct answer corresponding to $$\phi$$=$$\ 180$$$$\circ$$. What does the scattering angle imply?

Please check my work.

 

[neelakash]

I posted h(nu) times (1- cos phi)

and in the last but one line, phi=180 degree