Question

One milligram of matter converted into energy will give?
A. \[90{\text{ }}joule\]
B. $9 \times {10^3}{\text{ }}joule$
C. $9 \times {10^5}{\text{ }}joule$
D. $9 \times {10^{10}}{\text{ }}joule$

Answer 1

Hint In this question, use the conversion of any matter into its equivalent energy, and then we have to use the famous Einstein’s mass-energy equivalence relation. Use the unit conversion from milligram to kilogram.

 Complete step-by-step solution:
As per the above-given question, the mass is one milligram. We need to calculate the energy to cover the same given mass into energy. We apply the formula as stated above Einstein’s mass-energy equivalence.
First, convert the given values into MKS system which is standard and is also required as the given options are in joule.
Use the base units of the MKS system which stated as meter, kilogram, and second.
Given mass converted into kilogram is, ${\text{1 mg}} = {\text{1}}{{\text{0}}^{ - {\text{6}}}}{\text{ kg}}$.
\[E = m{c^2}\]
In the above given formula, $m$ is the mass of the matter and$c$ is the speed of light in a vacuum and takes the value of $c$ as \[3 \times {10^8}{\text{m/s}}\].
Substitute ${\text{1}}{{\text{0}}^{ - {\text{6}}}}{\text{ kg}}$ for $m$ and \[3 \times {10^8}{\text{m/s}}\] for $c$ in the above formula.
\[
  E = {10^{ - 6}}{\text{kg}} \times {\left( {3 \times {{10}^8}{\text{m/s}}} \right)^2} \\
  E = 9 \times {10^{10}}{\text{joule}} \\
 \]
Consider the speed of light as an invariant quantity because it will remain constant irrespective of the masses.

Therefore, the correct option is D.

Note:-
The energy of any given matter when converted into its equivalence energy is dependent on the mass of the matter as the speed of light is constant so use it carefully and do the calculation carefully and avoid silly mistakes.