Question

If the nuclear fission, piece of uranium of mass 5.0 g is lost, the energy obtained in kWh is
A. \[1.25 \times {10^7}\]
B. \[2.25 \times {10^7}\]
C. \[3.25 \times {10^7}\]
D. \[0.25 \times {10^7}\]

Answer 1

Hint: In this question, we need to use Einstein’s mass-energy equivalence principle. According to Einstein’s energy-mass equivalence principle, anything that has mass possesses an equivalent amount of energy and vice-versa. We can write the famous Einstein formula relating the mass and energy as; \[E = m{c^2}\].

Complete step by step answer:
Given:
The piece of the mass of uranium lost in nuclear fission is, m = 5.0 g = \[5 \times {10^{ - 3}}\;{\rm{kg}}\]
Now using the mass-energy equivalence formula, \[E = m \cdot {c^2}\].
Substituting the values of mass and the speed of light (\[c = 3 \times {10^8}{\rm{ m - }}{{\rm{s}}^{ - 1}}\]) in the above formula we have;
 \[\begin{array}{c}
E = m \cdot {c^2}\\
 = \left( {5.0 \times {{10}^{ - 3}}{\rm{ kg}}} \right) \cdot {\left( {3.0 \times {{10}^8}{\rm{m - }}{{\rm{s}}^{ - 1}}} \right)^2}\\
 = 45 \times {10^{13}}{\rm{ J}}\\
 = 4.5 \times {10^{14}}{\rm{ J}}
\end{array}\]
Again, \[1{\rm{ kWh}} = {\rm{3}}{\rm{.6}} \times {\rm{1}}{{\rm{0}}^6}{\rm{ J}}\].
So, \[E = \left( {4.5 \times {{10}^{14}}} \right)\left( {\dfrac{{1{\rm{ kWh}}}}{{3.6 \times {{10}^6}{\rm{ J}}}}} \right) = 1.25 \times {10^8}{\rm{ kWh}}\]
Therefore, the energy released is \[1.25 \times {10^8}\;{\rm{kWh}}\], and option (A) is the option closest to our answer. The option (A) needs to be multiplied by a factor of 10 to make it right. Additional Information: The mass-energy equivalence relation is applicable not only for nuclear fission reaction but also nuclear fusion reaction. The mass left unaccounted at the end of nuclear reactions is the mass that gets converted and released as energy (generally in the form of heat, light, or even both). We can explain the energy released from the reactors of nuclear power plants, the atom bomb, or even the energy released from the Sun with this relation.

Note: In this question, since we get the lost mass, we have directly applied the formula \[E = m{c^2}\]. If the lost mass is not available in the question, then we have to use the formula \[E = \Delta m{c^2}\], where \[\Delta m\] is the difference in the total mass of the reactants and the total mass of the products.