Question

According to Einstein’s equation \[E = m{c^2}\], E represents the rest mass energy of an object with rest mass m, c is the speed of light in vacuum, and it given by \[2.998 \times {10^8}\,m/s\]. Find the rest mass energy of an electron whose rest mass is \[9.11 \times {10^{ - 31}}\,kg\].
(A) \[8.18817 \times {10^{ - 14}}\,J\]
(B) \[8.18807 \times {10^{ - 14}}\,J\]
(C) \[8.18907 \times {10^{ - 14}}\,J\]
(D) \[8.19807 \times {10^{ - 14}}\,J\]

Answer 1

Hint:Substitute the given quantities of mass of electron and speed of light in vacuum in the given formula for rest mass energy. The Einstein equation, \[E = m{c^2}\] is applicable for any particle of non zero mass.

Formula used:
\[E = m{c^2}\]
Here, E represents the rest mass energy of an object with rest mass m, c is the speed of light in vacuum.

Complete step by step answer:
We have given that the rest mass energy of the object is given as,
\[E = m{c^2}\]
Here, m is the mass of the object and c is the speed of light.
We can determine the rest mass energy of the electron by substituting \[9.11 \times {10^{ - 31}}\,kg\] for m and \[2.998 \times {10^8}\,m/s\] for c in the above equation.
\[E = \left( {9.11 \times {{10}^{ - 31}}} \right){\left( {2.998 \times {{10}^8}} \right)^2}\]
\[ \therefore E = 8.18807 \times {10^{ - 14}}\,J\]

So, the correct answer is option (B).

Additional information:
Einstein proposed the concept of rest mass energy \[E = m{c^2}\]. This is the energy stored in any object due to its state of rest position. The energy confined in this object is due to the fact that it has a mass. Every object with mass has rest mass energy. We know that the rest mass of the photon is zero. Therefore, the photon has no rest mass energy. The term rest mass energy is essential to determine the kinetic energy of the objects with speed compared to the speed of light.

Note:The rest mass energy possessed by the object is constant even if it is moving. Since the speed of light is constant, the rest mass energy only depends on the mass of the object. The rest mass of the photon is zero. Therefore, the photon has zero rest mass energy.