A 0030 nm photon collides with a stationary electron After t

A 0.030 nm photon collides with a stationary electron. After the collision, the electron moves forward and the photon recoils backward. Find the momentum and the kinetic energy of the electron.

____keV/c

____ eV

Solution

The momentum of the inbound photon is:
p(photon) = E / c
p(photon) = (h c/lambda) / c
p(photon) = h/lambda
p(photon) = 6.626x10^-34 J s / 0.030nm
p(photon) = 22.088x10^-24 kg m/s

We can then use the Compton formula to find the recoil frequency and the momentum:
lambda(after) - lambda(before) = (h/m(e) c) (1 - cos(theta))

Assuming this is head-on, then cos(theta) is -1.
lambda(after) - lambda(before) = 2(h/m(e) c)
lambda(after) = 2(h/m(e) c) + lambda(before)
lambda(after) = 0.00485nm + 0.030nm
lambda(after) = 0.03485nm

E = h c/lambda
E(before) = h c / 0..030nm
E(before) = 41329eV
E(after) = h c / 0.03485nm
E(after) = 35577eV
dE = 41329-35577
dE = 5752eV

So the electron has the 5752eV that the photon gave up