First slide

Mass Energy equivalence

Question

Rest mass energy of a particle is 3 MeV and the particle is moving with a linear momentum of $2.133 \times 10^{- 21} K g - m / s$ . Then total energy of the particle is

Moderate

A

6 MeV
B

8 MeV
C

5 MeV
D

4 MeV

Solution

Total energy is given by ${(E)}^{2} = (m_{o} c^{2}) + {(p c)}^{2}$
Now, $m_{o} c^{2} = 3 M e V$
$p c = \frac{2.133 \times 10^{- 21} \times 3 \times 10^{8}}{1.6 \times 10^{- 19} \times 10^{6}} M e V = 4 M e V$
$∴ E = \sqrt{{(3)}^{2} + {(4)}^{2}} MeV = 5 MeV$

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