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