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:

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

The mass of a ${}_3{}^7\mathrm{Li}$ nucleus is \(0.042~\text{u}\) less than the sum of the masses of all its nucleons. The binding energy per nucleon of the ${}_3{}^7\mathrm{Li}$ nucleus is near:
1. \(4.6~\text{MeV}\)
2. \(5.6~\text{MeV}\)
3. \(3.9~\text{MeV}\)
4. \(23~\text{MeV}\)

The binding energy per nucleon in deuterium and helium nuclei are \(1.1\) MeV and \(7.0\) MeV, respectively. When two deuterium nuclei fuse to form a helium nucleus the energy released in the fusion is:
1. \(2.2\) MeV
2. \(28.0\) MeV
3. \(30.2\) MeV
4. \(23.6\) MeV

A nucleus ${}_Z{X}^A$ has a mass represented by \(M(A, Z).\) If \(M_P\) and \(M_n\) denote the mass of proton and neutron respectively and BE the binding energy, then:

1. $BE=\left[M\right(A,Z)-Z{M}_p-(A-Z\left)M_n\right]c^2$

2. $BE=[Z{M}_p+(A-Z)M_n-M(A,$ $Z\left)\right]c^2$

3. $BE=[Z{M}_p+A{M}_n-M-(A,$ $Z\left)\right]c^2$

4. $BE=M(A,$ $Z)-Z{M}_p-(A-Z)M_n$

The binding energy of deuteron is \(2.2~\text{MeV}\) and that of \(_2\mathrm{He}^{4}\) is \(28~\text{MeV}\). If two deuterons are fused to form one \(_{2}\mathrm{He}^{4}\), ${\mathrm{}}^{}$then the energy released is:
1. \(25.8~\text{MeV}\)
2. \(23.6~\text{MeV}\)
3. \(19.2~\text{MeV}\)
4. \(30.2~\text{MeV}\)

If in a nuclear fusion process. the masses of the fusing nuclei be \(m_1\) and \(m_2\) and the mass of the resultant nucleus be \(m_3,\) then:

A nucleus represented by the symbol ${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}$ has:

M_P denotes the mass of a proton and M_n that of a neutron. A given nucleus, of binding energy B, contains Z protons and N neutrons. The mass M(N, Z) of the nucleus is given by:
(c is the velocity of light )

1. M(N, Z) = NM_n + ZM_P + Bc²

2. M(N, Z) = NM_n + ZM_P – B/c²

3. M(N, Z) = NM_n + ZM_P + B/c²

4. M(N, Z) = NM_n + ZM_P – Bc²