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

1.	\(\beta^{+}, ~\alpha, ~\beta^{-}\)	2.	\(\beta^{-}, ~\alpha, ~\beta^{+}\)
3.	\(\alpha, ~\beta^{-},~\beta^{+}\)	4.	\(\alpha, ~\beta^{+},~\beta^{-}\)

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

If a \({}_{a}^{b}\mathrm{X}\) species emits firstly a positron, then two \(\alpha\) and two \(\beta\) and at last one \(\alpha\) is also emitted and finally converted into stable \({}_{d}^{c}\mathrm{Y}\) species, so the correct relation will be:
1. \(c = b-12, d = a-5\)
2. \(a = c-8, d = b-1\)
3. \(a = c-6, d = b-0\)
4. \(a = c-4, a = b-2\)

The mass number of a nucleus is:

The volume occupied by an atom is greater than the volume of the nucleus by a factor of about:
1. \(10\)
2. \(10^5\)
3. \(10^{10}\)
4. \(10^{15}\)