### You should know¶

#### Energy-momentum Relation¶

$$ \large E^2 = (pc)^2 + (mc^2)^2 $$where

$E$: total energy (relativistic energy)

$p$: momentum of magnitude

$m$: rest mass (invariant mass)

$c$: speed of light

### Solution¶

Total energy $E$ = 5.0 GeV

Momentum of magnitude $p$ = 4.9 GeV/c

Then,

$$ \large \begin{split} (m c^2)^2 & = E^2 - (pc)^2 \\ \\ & = (5.0 \text{ GeV})^2 - (4.9 \text{ GeV})^2 \\ \\ & = 25 - 24.01 \text{ (GeV)}^2 \\ \\ & = 0.99 \text{ (GeV)}^2 \end{split} $$Therefore, the rest mass of the particle is approximately

$$ \large m \simeq 1.0 \text{ GeV/c}^2 $$### Answer¶

(D) 1.0 GeV/c$^2$