The half-life of a positron is very short. it reacts with an electron, and the masses of both are converted to two gamma-ray photons. e+10 +0−1e⟶ this reaction is called an annihilation reaction. the mass of an electron or positron is 9.109×10−31 kg. (a) calculate the energy produced by the reaction between one electron and one positron. (b) assuming that the two γ-ray photons have the same frequency, calculate this frequency. j = hz

Explanation:

(a)   It is known that relation between energy and mass is as follows.

where,    E = energy

              m = mass

              c = speed of light = m/s

As it is given that mass is kg. So, putting the given values into the above formula as follows.

                       =

                       =

Therefore, we can conclude that the energy produced by the reaction between one electron and one positron is .

(b) When gamma ray photons are produced then they will have the same frequency. Relation between energy and frequency is as follows.

                    E =   ..... (1)

where,     h = plank's constant =

              = frequency

Also,     ........ (2)

Hence, equating equations (1) and (2) as follows.

                    =        

So,    

=

                            =

Thus, we can conclude that the frequency is .