The binding energy of a nucleus is a measure of its

We are given the following atomic masses:
$^{238}_{92}U = 238.05079 \; u$
$^{4}_{2}He = 4.00260 \; u$
$^{234}_{90}Th = 234.04363 \; u$
$^{1}_{1}H = 1.00783 \; u$
$^{237}_{91}Pa = 237.05121 \; u$
Here,the symbol $Pa$ represents the element protactinium $(Z=91)$.
$(a)$ Calculate the energy released during the alpha decay of $^{238}_{92}U$.
$(b)$ Show that $^{238}_{92}U$ cannot spontaneously emit a proton.

Consider the following nuclear reaction : $^{238}\text{U} \rightarrow ^{234}\text{Th} + ^4\text{He}$. Take masses of $^{238}\text{U}$, $^{234}\text{Th}$ and $^4\text{He}$ as $238.050 \text{ u}$, $234.043 \text{ u}$ and $4.003 \text{ u}$, respectively. The $Q$ value for the reaction, in $\text{keV}$, is : [Given : $1 \text{ u} = 931.5 \text{ MeV/c}^2$]

The atomic mass of ${ }_{6} C^{12}$ is $12.000000 \ u$ and that of ${ }_{6} C^{13}$ is $13.003354 \ u$. The required energy to remove a neutron from ${ }_{6} C^{13}$,if the mass of a neutron is $1.008665 \ u$,will be: (in $MeV$)

Given below are two statements. One is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A) :$ The binding energy per nucleon is found to be practically independent of the atomic number $A$,for nuclei with mass numbers between $30$ and $170$.
Reason $(R) :$ Nuclear force is long range.
In the light of the above statements,choose the correct answer from the options given below $:$

The binding energy per nucleon $v/s$ mass number curve for nuclei is shown in the figure. $w, x, y$ and $z$ are four nuclei indicated on the curve. The process that would release energy is: