Question

Rest mass energy of an electron is:
A. 1.02 MeV
B. 0.511 KeV
C. 0.511 MeV
D. 2.02 MeV

Answer 1

Hint: In physics, rest mass is one of the fundamental constants. Rest mass energy is energy described in the Einstein equation. ‘e’ trends for electron charge. M tends for mega which is equal to ${{10}^{6}}$. Volt is a unit of energy. The Einstein equation is the most famous equation. It stated that energy and mass are interchangeable and they are different forms of the same thing.

Complete step-by-step answer:
The rest mass of any electron substance is defined by ‘Einstein mass energy equivalence relation’.
According to relation of Einstein mass energy,
${{E}_{o}}={{m}_{o}}{{c}^{2}}$
Where,
${{c}^{2}}$= velocity of light which is $3\times {{10}^{8}}m/s$
${{m}_{o}}$=rest mass of an electron which is $9.11\times {{10}^{-31}}kg$
${{E}_{o}}$=rest mass energy
We know that Einstein equation is given by,
${{E}_{o}}={{m}_{o}}{{c}^{2}}$
Put value of rest mass of an electron and velocity of light in above equation,
We get,
${{E}_{o}}=9.11\times {{10}^{-31}}\times {{(3\times {{10}^{8}})}^{2}}$
Solve this we get,
${{E}_{o}}=8.91\times {{10}^{-14}}J----(1)$
We can convert joule into eV, as our options are also in eV.
We know that,
$1eV=1.6\times {{10}^{-19}}J$
So 1 joule (J) is equal to,
$1J=\dfrac{1eV}{1.6\times {{10}^{-19}}}$
Put above value in equation (1)
We get,
$\begin{align}
  & {{E}_{o}}=\dfrac{8.91\times {{10}^{-14}}}{1.6\times {{10}^{-19}}}eV \\
 & {{E}_{o}}=0.511\times {{10}^{6}}eV \\
 & {{E}_{o}}=0.511MeV \\
\end{align}$
Therefore, rest mass energy is given by${{E}_{o}}=0.511MeV$.
Answer- (c)

Note: SI unit of energy is joule. There are many conversions of energy in other units i.e. we can express energy in many units. Rest mass in relativity is a little different concept. Rest mass energy is dependent on rest mass and velocity of light in vacuum only. Relativistic mass is the mass which is assigned to the body in motion.