The binding energies of the nuclei A and B are E_a and E_b respectively. If three atoms of the element B fuse to give one atom of element A and an energy Q is released, then E_a, E_b and Q are related as:

1. E_a – 3E_b = Q

2. 3E_b – E_a = Q

3. E_a + 3E_b = Q

4. E_b + 3E_a = Q

A certain mass of Hydrogen is changed to Helium by the process of fusion. The mass defect in the fusion reaction is 0.02866 u. The energy liberated per nucleon is: (Given 1 u = 931 MeV)

The mass of a ${}_3{}^7\mathrm{Li}$ nucleus is 0.042 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 MeV

2. 5.6 MeV

3. 3.9 MeV

4. 23 MeV

In the nuclear decay given below: 
${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}\to {}_{\mathrm{Z}+1}{}^{\mathrm{A}}\mathrm{Y}\to {}_{\mathrm{Z}-1}{}^{\mathrm{A}-4}\mathrm{B}\to {}_{\mathrm{Z}-1}{}^{\mathrm{A}-4}\mathrm{B}$
the particles emitted in the sequence are:

If M (A, Z), ${\mathrm{M}}_p$, and ${\mathrm{M}}_n$ denote the masses of the nucleus ${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}$, proton, and neutron respectively in units of u (1 u = 931.5 MeV/c²) and BE represents its binding energy in MeV, then:

The binding energy of deuteron is 2.2 MeV and that of ${}_{2}H{e}^4$ is 28 MeV. If two deuterons are fused to form one ${}_{2}H{e}^4$ then the energy released is:

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

A nucleus with mass number 220 initially at rest emits an $\alpha$-particle. If the Q value of the reaction is 5.5 MeV, then the kinetic energy of $\alpha$-particle is:

1.  4.4 meV

2.  5.4 MeV

3.  5.6 MeV

4.  6.5 MeV

If the density of gold nucleus is X, then the density of silver nucleus will be:

1.  2X

2. $\frac{X}{3}$

3.  4X

4.  X 

The volume (V) of a nucleus is related to its mass (M) as:

1.  $V$ $\propto$ $M$

2.  $V$ $\propto$ $\frac{1}{M}$

3.  $V$ $\propto$ $M^3$

4.  $V$ $\propto$ $\frac{1}{M^3}$