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:

(0e+1)+ (0e-1)---> 2γ

(the 0 in front of e is the mass # and behind it is the atomic #)

(γ stands for the photons)

This reaction is called an annihilation reaction. the mass of an electrion or positron is 9.109 * 10^-31 kg

a) Calculate the energy produced by the reaction between one electron and one positron.( in Joules)

change in E= ______J

b)Assuming that the two γ-ray photons have the same frequency,calculate this frequency.

γ photon=_____Hz

Answer 1

(a)

E = (2)mc²
E = (2)(9.1 x 10^-31 kg)(3.00 x 10⁸)²
E = 1.638 x 10^-13 J

(b)

The two gamma ray photons have the same frequency.
h*f= E/2= mc² We solve for f,

(6.626 x 10^-34 J.s)(f) = (1.638 x 10^-13/ 2 )

f = 1.236 x 10²⁰ Hz

Thank you