# Chapter 26 - Problems - Page 1014: 84

$E = 2.56~MeV$

#### Work Step by Step

We can find $\gamma$: $\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$ $\gamma = \frac{1}{\sqrt{1-\frac{(0.600~c)^2}{c^2}}}$ $\gamma = \frac{1}{\sqrt{1-0.360}}$ $\gamma = 1.25$ We can find the mass of the particle: $E = \gamma~mc^2$ $m = \frac{E}{\gamma~c^2}$ $m = \frac{0.638~MeV}{(1.25)~c^2}$ $m = 0.5104~MeV/c^2$ We can find the new total energy: $E = \gamma~mc^2$ $E = ( \frac{1}{\sqrt{1-\frac{v^2}{c^2}}})~(mc^2)$ $E = ( \frac{1}{\sqrt{1-\frac{(0.980~c)^2}{c^2}}})~(0.5104~MeV/c^2)(c^2)$ $E = ( \frac{1}{\sqrt{1-(0.980)^2}})~(0.5104~MeV)$ $E = 2.56~MeV$

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