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BAlexanderSUS
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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!