Question

One microgram of matter converted into energy will give.
$\begin{align}
  & \text{A}\text{. 90}J \\
 & \text{B}\text{. }9\times 10J \\
 & \text{C}\text{. }9\times {{10}^{10}}J \\
 & \text{D}\text{. }9\times {{10}^{5}}J \\
\end{align}$

Answer 1

Hint: At first we need to see what values are given in the question. Now, we need to find the energy so we must apply the formula required for finding the binding energy or the energy mass equivalence. By applying this formula and then putting the values given to us we will figure out the exact answer.

Formula Used:
$E=m{{c}^{2}}$

Complete answer:
Here in the question we have to find the binding energy or the energy mass equivalence,
Now we know that the mass is given as one microgram.
We know that the formula for energy mass equivalence is,
$E=m{{c}^{2}}$
So, if mass is one microgram then it means that it is ${{10}^{-6}}Kg$ ,
Now taking the above formula,
$E={{10}^{-6}}\times {{\left( 3\times {{10}^{8}} \right)}^{2}}$
On solving the above equation we get,
$E=9\times {{10}^{10}}J$.
So by this result we see that if we convert one microgram into energy we get $9\times {{10}^{10}}J$.

So option C, is the correct option.

Additional Information:
In physics energy is nothing but a quantitative property and that must be transferred from one body to another and Energy cannot be destroyed. It will always change its form and stay in the system always, like we can change mechanical work into electrical energy and with this electrical energy we can again do some mechanical work.

Note:
In the equation $E=m{{c}^{2}}$, E is the energy, m is the mass given, and ‘c’ is actually the speed of light in vacuum. We must remember to convert all the units to their SI unit at first and then go ahead with the sum or the calculation.