Question

What is energy equivalent to a $10 \mu g$ mass?
(A) $9 \times {10^7}J$
(B) $3 \times {10^{11}}J$
(C) $5 \times {10^{11}}J$
(D) $7 \times {10^{11}}J$

Answer 1

Hint
Einstein’s energy formula stated that equivalent energy can be calculated by multiplying mass to square of the speed of light.

Complete step-by-step solution
Any substance or object having energy has a corresponding mass so, Equivalent energy is calculated using Einstein mass – energy relation.
$E = m{c^2}$
According to this equation-
$E$ is the equivalent energy,
$m$ is the mass of which energy is calculated,
$c$ is the speed of light.
From the given data, we know that
$m = 10\mu g$ $\;(\mu g = {10^6}g\;)$
$m = 10 \times {10^6}g$
$c$ value is known to us that is, $c = 3 \times {10^8}m{s^{ - 1}}$.
Now substitute the values in the mass energy relation to get the equivalent energy,
$
  E = 10 \times {10^6} \times {(3 \times {10^8})^2} \\
  \Rightarrow E = 10 \times {10^6} \times 9 \times {10^{16}} \\
  \Rightarrow E = 9 \times {10^9}J \\
 $
Hence, the equivalent energy is $9 \times {10^9}J$.
So, The correct option above is (A).

Note
In mass energy equivalence the total mass of the system may change but the total energy and momentum do not, they remain constant. In this equation Einstein tells that when atoms fuse together they create a great amount of energy.