\magnification=\magstep2


$$
\eqalign {
{{E_i}\over{c}} \quad &= \quad -{{E_f}\over{c}} 
                      \thinspace + \thinspace
                      \gamma m_e v \cr
\cr
E_i \thinspace + \thinspace m_e c^2 \quad &= \quad
                  E_f \thinspace + \thinspace \gamma m_e c^2 \cr
}
$$

$$
{{1}\over{E_f}} \quad = \quad {{1}\over{E_i}} 
                      \thinspace + \thinspace
                          {{2} \over {m_e c^2}} 
$$

$$
{{1}\over{E_f}} \quad \simeq \quad {{1}\over{\infty}} 
                      \thinspace + \thinspace
                          {{2} \over {m_e c^2}} 
$$

$$
E_f \quad \simeq \quad {{m_e c^2 } \over {2}}
$$


$$
{{E_i}\over{E_f}} \quad \simeq \quad {{1}\over{2}} \left ( 1 - {{v}\over{c}} 
                      \right ) 
$$

\bye

