If the total binding energies of ${ }_1^2 H ,{ }_2^4 He ,{ }_{26}^{56} Fe$ and ${ }_{92}^{235} U$ nuclei are $2.22, 28.3, 492$ and $1786 \text{ MeV}$ respectively,identify the most stable nucleus of the following.

If $M_o$ is the mass of an oxygen isotope $_8O^{17}$,$M_p$ and $M_N$ are the masses of a proton and a neutron respectively,the nuclear binding energy of the isotope is

The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be $E_b^p$ and the binding energy of a neutron be $E_b^n$ in the nucleus. Which of the following statement(s) is(are) correct?
$(A)$ $E_b^p - E_b^n$ is proportional to $Z(Z-1)$ where $Z$ is the atomic number of the nucleus.
$(B)$ $E_b^p - E_b^n$ is proportional to $A^{-1/3}$ where $A$ is the mass number of the nucleus.
$(C)$ $E_b^p - E_b^n$ is positive.
$(D)$ $E_b^p$ increases if the nucleus undergoes a beta decay emitting a positron.

The binding energy per nucleon of ${ }_{8}^{16}O$ is $7.97 \text{ MeV}$ and that of ${ }_{8}^{17}O$ is $7.75 \text{ MeV}$. The energy required to remove one neutron from ${ }_{8}^{17}O$ is $\qquad \text{ MeV}$.

From the given data,the amount of energy required to break the nucleus of aluminium ${ }_{13}^{27} {Al}$ is $x \times 10^{-3} {J}$.
Mass of neutron $= 1.00866 \, {u}$
Mass of proton $= 1.00726 \, {u}$
Mass of aluminium nucleus $= 26.98154 \, {u}$
(Assume $1 \, {u}$ corresponds to $1 \, {J}$ of energy for the purpose of this calculation)
(Round off to the nearest integer)

If the binding energy of $N^{14}$ is $7.5 \text{ MeV}$ per nucleon and that of $N^{15}$ is $7.7 \text{ MeV}$ per nucleon, then the energy required to remove a neutron from $N^{15}$ is (in $\text{ MeV}$)