Respuesta :
Explanation:
(a) It is known that relation between energy and mass is as follows.
[tex]E = 2 \times mc^{2}[/tex]
where, E = energy
m = mass
c = speed of light = [tex]3 \times 10^{8}[/tex] m/s
As it is given that mass is [tex]9.109 \times 10^{-31}[/tex] kg. So, putting the given values into the above formula as follows.
[tex]E = 2 \times mc^{2}[/tex]
= [tex]2 \times 9.109 \times 10^{-31} kg \times 3 \times 10^{8}m/s[/tex]
= [tex]1.638 \times 10^{-13} J[/tex]
Therefore, we can conclude that the energy produced by the reaction between one electron and one positron is [tex]1.638 \times 10^{-13} J[/tex].
(b) When gamma ray photons are produced then they will have the same frequency. Relation between energy and frequency is as follows.
E = [tex]h \times \nu[/tex] ..... (1)
where, h = plank's constant = [tex]6.626 \times 10^{-34} J.s[/tex]
[tex]\nu[/tex] = frequency
Also, [tex]E = 2 \times mc^{2}[/tex] ........ (2)
Hence, equating equations (1) and (2) as follows.
[tex]h \times \nu[/tex] = [tex]2 \times mc^{2}[/tex]
So,
[tex]6.626 \times 10^{-34} Js \times \nu[/tex] = [tex]1.638 \times 10^{-13} J[/tex]
[tex]\nu[/tex] = [tex]1.236 \times 10^{20} Hz[/tex]
Thus, we can conclude that the frequency is [tex]1.236 \times 10^{20} Hz[/tex].
