Question

If 1mg of ${U^{235}}$ is annihilated the energy liberated is –
(A) $9 \times {10^{10}}J$
(B) $9 \times {10^{19}}J$
(C) $9 \times {10^{18}}J$
(D) $9 \times {10^{17}}J$

Answer 1

Hint:The Uranium \[235\] is a heavy metal that has been used as an abundant source of concentrated energy for over \[60\] years. Uranium transmitted energy so we use it in nuclear fission and fusion, here the given problem said how much energy if formed so to find this we have to use the mass-energy equivalence theory of Einstein.

Complete step by step answer:
From Einstein’s mass-energy equivalence relation, we can say that $E = m{c^2}$
Where E is the energy liberate, m is the mass vacuum, \[e\] is speed of light in medium
So, by the given problem
$
  m = 1mg = {10^{ - 6}} kg \\
  c = 3 \times {10^8} m/s \\
$
So, energy liberated \[ = E = m{c^2}\]
$
   = {10^{ - 6}} \times {\left( {3 \times {{10}^8}} \right)^2} \\
   = {10^{ - 6}} \times 9 \times {10^{16}} \\
   = 9 \times {10^{16 - 6}} \\
   = 9 \times {10^{10}}J \\
$
So, option (A) is correct.

Note:From Einstein’s theory of relativity energy is equal to the product of mass and square of light i.e. $E = m{c^2}$, which expresses that energy and mass can be changed into each other. So, when to find energy or mass from relatives. We can use this formula. By this energy liberation, Atomic bomb is produced. In that case, ${U^{235}}$ become destroyed and produce huge energy.