The disintegration energy $Q$ for the nuclear fission of ${ }^{235} U \rightarrow{ }^{140} Ce+{ }^{94} Zr+n$ is $\_ \text{MeV}$.
Given atomic masses of:
${ }^{235} U: 235.0439 \text{ u}, { }^{140} Ce: 139.9054 \text{ u},$
${ }^{94} Zr: 93.9063 \text{ u}, n: 1.0086 \text{ u},$
Value of $c^2 = 931 \text{ MeV/u}$.

$U^{235}$ 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 $144 \times 10^4 \text{ s}$, then 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 $\text{ kg}$)

When $^{235}_{92}U$ is bombarded with one neutron,fission occurs and the products are three neutrons,$^{94}_{36}Kr$ and:

Solar energy is mainly caused due to

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.

The operation of a nuclear reactor is said to be critical when the value of the neutron multiplication factor $K$ is: