The decrease in the mass of Uranium in a nuclear reactor operating at a power of $12 \text{ MW}$ per day is (Energy released in one ${}_{92}U^{235}$ fission is about $200 \text{ MeV}$):

$A$ $^{235}U$ nuclear reactor generates energy at a rate of $3.70 \times 10^7 \text{ J/s}$. Each fission liberates $185 \text{ MeV}$ of useful energy. If the reactor has to operate for $144 \times 10^4 \text{ s}$, the mass of the fuel needed is (Assume Avogadro's number $= 6 \times 10^{23} \text{ mol}^{-1}$, $1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}$) (in $\text{ kg}$)

If the binding energy per nucleon of deuteron $({ }_1 H^2)$ is $1.15 \text{ MeV}$ and an $\alpha$-particle has a binding energy of $7.1 \text{ MeV}$ per nucleon,then the energy released per nucleon in the given reaction is ${ }_1 H^2 + { }_1 H^2 \rightarrow { }_2 He^4 + Q$. (in $\text{ MeV}$)

In a nuclear reactor,the main purpose of the moderator is to

When a proton collides with a $_3Li^7$ nucleus and results in a $_4Be^8$ nucleus,the emitted particle is:

What is a nuclear chain reaction? Explain the difficulties and their removal for its successful operation.