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 MeV. The total gain in the binding energy in the process is:

1. 804 MeV 

2. 216 MeV 

3. 0.9 MeV 

4. 9.4 MeV 

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 half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be:

1. $\frac{2}{3}$

2. $\frac{2}{3\sqrt{2}}$

3. $1/2$

4. $\frac{1}{2\sqrt{2}}$

The energy equivalent of 0.5 g of a substance is:

1. $4.5\times {10}^{13} J$

2. $1.5\times {10}^{13} J$

3. $0.5\times {10}^{13} J$

4. $4.5\times {10}^{16} J$

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?

The half-life of a radioactive sample undergoing \(\alpha- \text{decay}\) is $1.4\times {10}^{17} \sec$. If the number of nuclei in the sample is $2.0 \times {10}^{21}$, the activity of the sample is nearly equal to:

1.  ${10}^4 Bq$

2.  ${10}^5 Bq$

3.  ${10}^6 Bq$

4.  ${10}^3 Bq$

The rate of radioactive disintegration at an instant for a radioactive sample of half-life 2.2 $\times {10}^{9}s is {10}^{10} s^{-1}$. The number of radioactive atoms in that sample at that instant is:

1. 3.7$\times {10}^{20}$

2. 3.17$\times {10}^{17}$

3. 3.17$\times {10}^{18}$

4. 3.17$\times {10}^{19}$