- #1
niehls
- 25
- 0
there is this problem which I'm having problems solving.
An X-ray beam has an energy of 40keV. Find the maximum possible kinetic energy of Compton scattered electrons.
The electron is initially at rest.
I go at it this way.
For maximum momentum to be delivered from the photon to the electron, the collision must be straight on, reflecting the photon by an angle 180 degrees.
Photon momentum:
before collision: p = E/c
after collision: p = -E/c
if positive direction is along the photon's initial path.
This means the difference in momentum is 2E/c. This momentum must be transferred to the electron (conservation of momentum). Using K = E_total - mc^2, p = 2E/c and
E_total^2 = (pc)^2 + (mc^2)^2
This yields K = 6.22keV. The correct answer is 5.47 keV. Could someone please help and point me in the right direction...
thanks
An X-ray beam has an energy of 40keV. Find the maximum possible kinetic energy of Compton scattered electrons.
The electron is initially at rest.
I go at it this way.
For maximum momentum to be delivered from the photon to the electron, the collision must be straight on, reflecting the photon by an angle 180 degrees.
Photon momentum:
before collision: p = E/c
after collision: p = -E/c
if positive direction is along the photon's initial path.
This means the difference in momentum is 2E/c. This momentum must be transferred to the electron (conservation of momentum). Using K = E_total - mc^2, p = 2E/c and
E_total^2 = (pc)^2 + (mc^2)^2
This yields K = 6.22keV. The correct answer is 5.47 keV. Could someone please help and point me in the right direction...
thanks
Last edited: