Question

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⟶2???? 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 ????photon= Hz

Answer 1

Explanation:

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

            $E = 2 \times mc^{2}$

where,    E = energy

              m = mass

              c = speed of light = $3 \times 10^{8}$ m/s

As it is given that mass is $9.109 \times 10^{-31}$ kg. So, putting the given values into the above formula as follows.

             $E = 2 \times mc^{2}$

                       = $2 \times 9.109 \times 10^{-31} kg \times 3 \times 10^{8}m/s$

                       = $1.638 \times 10^{-13} J$

Therefore, we can conclude that the energy produced by the reaction between one electron and one positron is $1.638 \times 10^{-13} J$.

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

                    E = $h \times \nu$   ..... (1)

where,     h = plank's constant = $6.626 \times 10^{-34} J.s$

              $\nu$ = frequency

Also,     $E = 2 \times mc^{2}$ ........ (2)

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

                    $h \times \nu$ = $2 \times mc^{2}$        

So,    

$6.626 \times 10^{-34} Js \times \nu$ = $1.638 \times 10^{-13} J$

                           $\nu$ = $1.236 \times 10^{20} Hz$

Thus, we can conclude that the frequency is $1.236 \times 10^{20} Hz$.