Now apply energy conservation

PHYSICS · Subjective · AP · Physics 2: Algebra-based · Modern Physics · Modern Physics

Problem

Now apply energy conservation. You will need the result from relativity that the total energy of an electron of momentum

p

is given by

E = \sqrt{p^2 c^2 + (mc^2)^2}

. What is the total energy of an electron at rest? Therefore deduce that energy conservation leads to

\frac{hc}{\theta} + mc^2 = \frac{hc}{\theta'} + \sqrt{p^2 c^2 + (mc^2)^2}