Question

When a slow neutron is captured by a $_{92}^{235} U$ nucleus, a fission energy released is 200 MeV. If power of nuclear reactor is 100 W then rate of nuclear fission is:
A. $3.6 \times 10^6 s^{-1}$
B. $3.1 \times 10^{12} s^{-1}$
C. $1.8 \times 10^4 s^{-1}$
D. $4.1 \times 10^6 s^{-1}$

Answer 1

Hint: The energy generated by 1 fission reaction has to be converted to standard units first as power generated is given in Watts. Power generated is the amount of energy generated in 1 second.

Complete step by step answer:
We are given that one reaction produces 200 MeV energy. We first convert this into Joules.
Since 1 eV = $1.6 \times 10^{-19}$ J, we can write,
$200 MeV = 200 \times 10^6 \times 1.6 \times 10^{-19} J = 3.2 \times 10^{-11} J$.

Now, rate of energy generation in nuclear reactor is given as 100 W. Therefore, the number of reactions occurring in 1 second can be found as:
$\dfrac{100}{3.2 \times 10^{-11} } = 3.125 \times 10^{12} $

Therefore, the correct answer is option (B).

Additional information:
The energy generated in fission reaction is due to the fragmentation of unstable Uranium nucleus by an incident thermal neutron. If we have a sample of Uranium and we have too many neutrons as a reaction product, like the average number is about 3 neutrons in a reaction, we find an uncontrolled reaction occurring in the sample as the neutrons keep on multiplying and keep reacting further. Such reactions produce massive amounts of energy in very small amounts of time. In reactors, too avoid such occurrences; the reactions are controlled by various mechanisms, like by absorbing extra neutrons.

Note:
Rate of nuclear fission is nothing but the number of fission reactions taking place, which is what we had to find here. It can be a little confusing to remember the conversion from eV to J. One must remember that Joules is the bigger unit, electron Volts is much smaller than Joules. Also, one can remember conversion by considering the 'e' in electron volts. If we just put the value of constant e in place of that e, we find the energy in Joules.