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:

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. \(30.2~\text{MeV}\)

\(M_p\) 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. \(M(N,Z)= NM_n+ZM_p+ Bc^2\)
2. \(M(N,Z)= NM_n+ZM_p-\frac{B}{c^2}\)
3. \(M(N,Z)= NM_n+ZM_p+\frac{B}{c^2}\)
4. \(M(N,Z)= NM_n+ZM_p- Bc^2\)