First slide

Mass Energy equivalence

Question

Two antiparticles x and y at rest combine and as a result two gamma photons are produced. If total energy of the gamma photons is 1.022 MeV, mass of each particle is

Easy

A

$9.1 \times 10^{- 31} k g$
B

$1.67 \times 10^{- 27} k g$
C

$1.8 \times 10^{- 27} k g$
D

$7.2 \times 10^{- 30} k g$

Solution

Initial momentum of the antiparticles is zero. So by the principle of conservation of linear momentum, the photons must be moving in opposite directions with same magnitude of momentum. So the energy of the photons must be the same. Now the antiparticles must have the same mass.
$∴ 2 m \times {(3 \times 10^{8})}^{2} = 1.022 \times 10^{6} \times 1.6 \times 10^{- 19} \Rightarrow m = 9.1 \times 10^{- 31}$

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