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Question: The energy released per fission of Uranium is \({\text{ }}200{\text{ MeV }}\). Determine the number ...

The energy released per fission of Uranium is  200 MeV {\text{ }}200{\text{ MeV }}. Determine the number of fissions per second required to generate  2 MW {\text{ }}2{\text{ MW }} power.
A)  6.25×1016{\text{ }}6.25 \times {10^{16}}
B)  0.25×1016{\text{ }}0.25 \times {10^{16}}
C)  1.25×1016{\text{ }}1.25 \times {10^{16}}
D)  25×1016{\text{ }}25 \times {10^{16}}

Explanation

Solution

** Nuclear fission is the process of splitting of a heavy nucleus into two or more, smaller fragments and also some particles as by-products. A huge amount of energy is released during this process. Uranium is the most common radioactive heavy nucleus that undergoes nuclear fission. From the given total energy released by uranium fission, we have to calculate the number of fissions.

Complete step by step solution:
The total energy released per fission of Uranium is given by, E=200 MeV{\text{ }}E = 200{\text{ MeV}}
To convert  MeV {\text{ }}MeV{\text{ }}into  eV {\text{ }}eV{\text{ }}we have to multiply the given value with  106 {\text{ }}{10^6}{\text{ }} and the value of  1 eV=1.6×10−19J {\text{ }}1{\text{ }}eV = 1.6 \times {10^{ - 19}}J{\text{ }}
Convert the given energy in MeV {\text{ }}MeV{\text{ }} to watt - seconds {\text{ watt - seconds }}, we get
E=200 Mev = 200×106×1.6×10−19watt - secondsE = 200{\text{ Mev = 200}} \times {\text{1}}{{\text{0}}^6} \times 1.6 \times {10^{ - 19}}{\text{watt - seconds}}
E=3.2×10−11JE = 3.2 \times {10^{ - 11}}J
The required energy per second  Er=2 MW{\text{ }}{E_r} = 2{\text{ MW}}
Converting this energy into watts, we get
Er=2 MW = 2×106W{E_r} = 2{\text{ MW = 2}} \times {\text{1}}{{\text{0}}^6}W
The number of fission per second can be obtained by dividing the total energy released in one second by the energy released per fission
Number of fission per second, N=ErE=2×1063.2×10−11=6.5×1016{\text{ }}N = \dfrac{{{E_r}}}{E} = \dfrac{{2 \times {{10}^6}}}{{3.2 \times {{10}^{ - 11}}}} = 6.5 \times {10^{16}}

The correct answer is Option (A): 6.25×1016{\text{ }}6.25 \times {10^{16}}.

Note: Compared with chemical reactions, nuclear reactions produce large energies. When the heavy nucleus is split into fragments, the mass of the parent nucleus will be greater than the sum of masses of the product nucleus and the by-products. This difference in mass is converted into energy. This conversion of mass into energy is explained by Einstein with the famous mass-energy equation  e=mc2 {\text{ }}e = m{c^2}{\text{ }}. Nuclear fission is a kind of elemental transmutation, where one element is converted into another by changing the atomic number. The energy released by one gram of uranium or plutonium per day liberates more energy than  3 tons {\text{ }}3{\text{ tons }} coal.