## College Physics (4th Edition)

$\gamma = 1.08$
We can find the kinetic energy of the protons: $K = q~\Delta V$ $K = (1.6\times 10^{-19}~C)(75\times 10^6~V)$ $K = 1.2\times 10^{-11}~J$ We can find the Lorentz factor $\gamma$: $K = (\gamma-1)~m_0~c^2$ $\gamma = 1+\frac{K}{m_0~c^2}$ $\gamma = 1+\frac{ 1.2\times 10^{-11}~J}{(1.67\times 10^{-27}~kg)(3.0\times 10^8~m/s)^2}$ $\gamma = 1.08$