If the average number of neutrons liberated per fission is $2.5$ and energy released per fission is $250 \, MeV$, then the number of neutrons generated per second in a nuclear reactor of $100 \, MW$ will be:

Which one of the following statements about uranium is correct?

Which of the following statement$(s)$ is/are correct?
$(1)$ The rest mass of a stable nucleus is less than the sum of the rest masses of its constituent nucleons.
$(2)$ The rest mass of a stable nucleus is greater than the sum of the rest masses of its constituent nucleons.
$(3)$ Nuclear fusion involves the fusion of two light nuclei to form a heavier nucleus.
$(4)$ Nuclear fission involves the release of energy by the splitting of a heavy nucleus.

When Uranium is bombarded with neutrons,it undergoes fission. The fission reaction can be written as ${}_{92}U^{235} + {}_0n^1 \to {}_{56}Ba^{141} + {}_{36}Kr^{92} + 3x + Q$,where three particles named $x$ are produced and energy $Q$ is released. What is the name of the particle $x$?

$A$ $^{235}U$ 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 $\text{ kg}$)

The binding energy of deuteron $_1^2H$ is $1.112 \, MeV$ per nucleon and an $\alpha$-particle $_2^4He$ has a binding energy of $7.047 \, MeV$ per nucleon. Then in the fusion reaction $_1^2H + _1^2H \to _2^4He + Q$,the energy $Q$ released is ........ $MeV$.