Question

An electron and a position may annihilate one another producing two $\gamma -$ ray photons of equal energy. the minimum energy of each of these photon is

• A. $8.2\times {10}^{-14}MeV$
• B. $8.2\times {10}^{-14}J$
• C. $16.4\times {10}^{-14}MeV$
• D. $16.4\times {10}^{-14}J$

Answer 1

The correct option is D $16.4\times {10}^{-14}J$

When these particle annihilate then their mass get converted in energy and their kinetic energy also get added in the

produced energy so the produced energy will be minimum when the annihilating particles don't have any kinetic energy

so in that case the energy released $E=(m+m)931.5Mev=2m\times 931.5Mev$ where $m$ is mass of positron or electron, both are equal.

Put $m=.000548amu$

we get $E=1.02Mev=1.02\times 1.6\times {10}^{-13}J=16.32\times {10}^{-14}J$

Option D is correct.