## College Physics (4th Edition)

(a) Since the kinetic energy is a significant fraction of the rest energy, the electrons are relativistic. (b) $v = 0.63~c$
(a) The rest energy of an electron is $511~keV$ and the kinetic energy is $150~keV$. Since the kinetic energy is a significant fraction of the rest energy, the electrons are relativistic. (b) We can find the Lorentz factor $\gamma$: $K = mc^2~(\gamma-1)$ $\gamma = \frac{K}{mc^2}+1$ $\gamma = \frac{150~keV}{511~keV}+1$ $\gamma = 1.2935$ We can find the speed: $\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$ $\sqrt{1-\frac{v^2}{c^2}} = \frac{1}{\gamma}$ $1-\frac{v^2}{c^2} = (\frac{1}{\gamma})^2$ $\frac{v^2}{c^2} = 1-(\frac{1}{\gamma})^2$ $v = \sqrt{1-(\frac{1}{\gamma})^2}~c$ $v = \sqrt{1-(\frac{1}{1.2935})^2}~c$ $v = 0.63~c$