there is this problem which i'm having problems solving.(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Compton scattered electron

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