A nucleus with mass number \(240\) breaks into fragments each of mass number \(120\). The binding energy per nucleon of unfragmented nuclei is \(7.6\) MeV while that of fragments is \(8.5~\text{MeV}\). The total gain in the binding energy in the process is:

A radioactive nucleus ${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}$ undergoes spontaneous decay in the sequence ${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}$ $\to {}_{\mathrm{z}-1}\mathrm{B}$ $\to$ ${}_{\mathrm{z}-3}\mathrm{C}$ $\to {}_{\mathrm{z}-2}\mathrm{D}$, where Z is the atomic number of element X. The possible decay particles in the sequence are: 

1. ${\mathrm{\beta }}^{+},$ $\mathrm{\alpha },$ ${\mathrm{\beta }}^{-}$

2. ${\mathrm{\beta }}^{-},$ $\mathrm{\alpha },$ ${\mathrm{\beta }}^{+}$

3. $\mathrm{\alpha },$ $$ ${\mathrm{\beta }}^{-},$ ${\mathrm{\beta }}^{+}$

4. $\mathrm{\alpha },$ $$ ${\mathrm{\beta }}^{+},$ ${\mathrm{\beta }}^{-}$

The energy equivalent of \(0.5\) g of a substance is:
1. \(4.5\times10^{13}\) J
2. \(1.5\times10^{13}\) J
3. \(0.5\times10^{13}\) J
4. \(4.5\times10^{16}\) J

When a uranium isotope ${}_{92}{}^{235}U$  is bombarded with a neutron, it generates  ${}_{36}{}^{89}Kr,$ three neutrons and: 

1. ${}_{40}{}^{91}Zr$

2. ${}_{36}{}^{101}Kr$

3. ${}_{36}{}^{103}Kr$

4. ${}_{56}{}^{144}Ba$

What happens to the mass number and the atomic number of an element when it emits \(\gamma\)-radiation?

If the radius of \(\mathrm{Al}\) nucleus is taken to be \(\mathrm{R}_{\mathrm{Al}},\) then the radius of ${\mathrm{Te}}_{53}^{125}$ nucleus is near:
1. ${\left(\frac{53}{13}\right)}^{\frac{1}{3}}{\mathrm{R}}_{\mathrm{Al}}$

The Binding energy per nucleon of \(^{7}_{3}Li\) and \(^{4}_{2}He\) nucleon are \(5.60~\text{MeV}\) and \(7.06~\text{MeV}\), respectively. In the nuclear reaction \(^{7}_{3}Li + ^{1}_{1}H \rightarrow ^{4}_{2}He + ^{4}_{2}He +Q\), the value of energy \(Q\) released is:
1. \(19.6~\text{MeV}\)
2. \(-2.4~\text{MeV}\)
3. \(8.4~\text{MeV}\)
4. \(17.3~\text{MeV}\)