Compton Effect (scattered photon angle)

  • #1

Homework Statement



Show that for Compton Effect: tan(ϴ) = (sinφ)/[(Δλ/λ) + (1-cosφ)]

Where,
ϴ = angle that the scattered photon makes with the incident photon
φ = angle that hte scattered electron makes with the incident photon

Homework Equations



For Photon:

initial;
E=hv
p=hv/c
(where v is frequency)

final;
E=hvʹ
p=hvʹ/c

For Electron;

initial;
E=mc^2
p=0

final;
p=p
E=sqrt(m^2c^4+p^2c^2)

note* (changed the v/c to 1/λ)


The Attempt at a Solution



Breaking the problem into components and solving for ϴ such that tanϴ=sinϴ/cosϴ:

X; (h/λ) = (h/λʹ)cosϴ +Pcosφ
Y; 0=(h/λʹ)sinϴ-Psinφ

so,

cosϴ=[((h/λ)-Pcosφ)λʹ]/h
sinϴ=Psinφ(λʹ)/h

tanϴ=sinϴ/cosϴ

so,

tanϴ=Psinφ/((h/λ)-Pcosφ)

from here I am lost, I'm assuming that there must be an property of momentum that I am not taking into account. Any help would be appreciated! thank you!
 

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