Question

Energy equal to mass of one electron is:
A. $8.2\text{ }\times \text{ 1}{{\text{0}}^{-7}}erg$
B. $9.2\times {{10}^{-7}}erg$
C. $8.2\times {{10}^{-10}}erg$
D. $4.1\times {{10}^{-8}}erg$

Answer 1

Hint: Use Einstein’s theory of relativity equation i.e. $E=m{{c}^{2}}$. This equation was derived from a principle that states that anything in this universe that has mass will have an equivalent amount of energy in it.

Complete step by step answer:
According to Einstein’s equation that is $E=m{{c}^{2}}$
Where
m= Mass of one electron i.e.$9.1\times {{10}^{-31}}kg$
c=speed of light =$3\times {{10}^{8}}m/s$
Therefore, putting the values in the equation
=$9.1\times {{10}^{-31}}\times {{(3\times {{10}^{8}})}^{2}}$
=$\dfrac{81.9\times {{10}^{-23}}kg{{m}^{2}}{{s}^{-2}}}{{{10}^{-7}}}$
=$8.2\times {{10}^{-7}}erg$
Hence the energy is equal to mass of one electron is $8.2\times {{10}^{-7}}erg$
So, the correct answer is “Option D”.

Note: Mass-energy equivalence is the principle that anything having mass has an equivalent amount of energy and vice versa
This formula states that mass has an energy which can be calculated by multiplying the mass and square of speed of light. This formula also states that every object at rest has a huge amount of intrinsic energy in it. According to Einstein mass and energy are two names for the same concept. According to him, the law of conservation of mass and law of conservation of energy are one at the same thing. This concept also shows how these things are interchangeable and. To come up with a single equation he considered that C i.e. speed of light is constant .In today’s world also we use this equation to solve many of our life problems .
Many diagnoses use this theorem for scanning and other purposes . The main test of cancer detection that is PET scan also uses this.