Question

The rest energy of electron or positron is
A). 0.51 MeV
B). 1 MeV
C). 1.02 MeV
D). 1.5 MeV

Answer 1

Hint: Every body possesses an energy called mass energy. Rest mass energy of a body is the energy possessed by the body when its mass is equal to its rest mass. Rest mass is the mass of the body when it is at rest.

Formula used: $m={{m}_{\circ }}\dfrac{1}{\sqrt{1-\dfrac{{{v}^{2}}}{{{c}^{2}}}}}$.

Complete step by step answer:
According to the theory of relativity, mass of a body changes with its motion and is given as $m={{m}_{\circ }}\dfrac{1}{\sqrt{1-\dfrac{{{v}^{2}}}{{{c}^{2}}}}}$, where m is the mass of the body at a speed of v, ${{m}_{\circ }}$ is the rest mass of the body (mass of the body at v=0) and c is the speed of light ($c=3\times {{10}^{8}}m{{s}^{-1}}$). ..……..(1)
It is said that mass is equivalent to energy and is called mass energy. Every body of mass m possess an energy E equal to $m{{c}^{2}}$. ……..………(2)
From statement (1), as the speed of a body increases its mass increases and the body reaches a speed that is almost equal to speed of light, the mass of the body reaches infinity.
From statement (2), as mass increases its energy will increase. Therefore, from statement (1) and statement (2), as the speed of the body reaches closer to the speed of light, the mass reaches to infinity and the energy of the body will reach to infinity.
Therefore, if a body wants to travel at a speed equal to the speed of light, it needs an infinite amount of energy. However, it is impossible to have an infinite amount of energy. Therefore, a body can never travel at a speed equal to the speed of light.
The rest mass of an electron is ${{m}_{\circ }}=9.11\times {{10}^{-31}}kg$.
Therefore, its rest mass energy is $E={{m}_{\circ }}{{c}^{2}}=9.11\times {{10}^{-31}}\times {{\left( 3\times {{10}^{8}} \right)}^{2}}=81.99\times {{10}^{-15}}J$.
The energy that we calculated is in joules and the options have the units of MeV. MeV means mega electron volts. 1 eV is equal to the energy when an electron of charge e passes through a potential difference of 1 volt and 1 MeV is equal to $1\times {{10}^{6}}eV$.
$1MeV=1.60\times {{10}^{-13}}J$. Therefore, $1J=\dfrac{1}{1.60\times {{10}^{-13}}}MeV$.
Let us write \[81.99\times {{10}^{-15}}J\] in the unit of MeV.
$81.99\times {{10}^{-15}}J=81.99\times {{10}^{-15}}.\left( \dfrac{1}{1.60\times {{10}^{-13}}}MeV \right)=0.51MeV$.
Therefore, the rest mass energy of an electron is 0.51MeV.
Hence, the correct option is (A).

Note: We solved this problem according to Albert Einstein’s theory of relativity. The whole theory is based on a primary assumption that speed of light is the fastest speed that any body in the universe can attain.