Question

The energy equivalent of the $E=m{{c}^{2}}$ matter in joule is given as,
$\begin{aligned} & A{{.10}^{17}} \\\ & B{{.19}^{20}} \\\ & C{{.10}^{11}} \\\ & D{{.10}^{14}} \\\ \end{aligned}$

Answer 1

the relation between the mass and the energy has been explained using Einstein's mass energy relationship. This tells that the energy is equivalent to the product of the mass and the square of the velocity of the light. This relation is to be used here by substituting the required parameters. Hope this will help you to solve this question.
Formula used:
$E=m{{c}^{2}}$
Where $m$be the mass to be converted into energy, $c$ be the velocity of light and $E$ be the energy produced.

Complete answer:
In the question it is mentioned to convert $E=m{{c}^{2}}$ mass into energy and express it in joules.
According to Einstein's mass energy relation tells that anything which is having a mass can have an energy equivalent to it and the vice versa is also true.
Therefore we can write that,
The equation for Einstein’s mass energy relationship is
$E=m{{c}^{2}}$
It has been given that the mass to be converted is,
$m=1Kg$
And velocity of the light is a constant which is given as,
$c=3\times {{10}^{8}}m{{s}^{-1}}$
Substituting these values in the equation will give,
$\Rightarrow E=1\times {{\left( 3\times {{10}^{8}} \right)}^{2}}=9\times {{10}^{16}}J$
This value of the energy can be expressed also as,
$\Rightarrow E=9\times {{10}^{16}}J\approx {{10}^{17}}J$

So, the correct answer is “Option A”.

Note:
The special theory of relativity by Einstein is explaining the concept of mass energy relationship. In this theory he is explaining mass as the concentrated energy. The theory of special relativity says that the velocity of light in vacuum is constant. The theory is explaining the relationship between the space and time. It also tells that all the observers in any of the reference frames are perceiving the same laws of nature. This theory is having a lot of significance in the field of quantum mechanics.