Mass numbers of the elements $A, B, C$ and $D$ are $30, 60, 90$ and $120$ respectively. The specific binding energies of them are $5 \text{ MeV}, 8.5 \text{ MeV}, 8 \text{ MeV}$ and $7 \text{ MeV}$ respectively. In which of the following reaction$(s)$ is energy released?
$1. D \rightarrow 2B$
$2. C \rightarrow B + A$
$3. B \rightarrow 2A$

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.

What does the binding energy per nucleon show?

The energy in $MeV$ released due to the complete transformation of $1\, kg$ of mass into energy is $(c = 3 \times 10^8\, m/s)$:

The energy equivalent to a substance of mass $1 \,g$ is

For a nucleus ${ }_Z^A X$ having mass number $A$ and atomic number $Z$:
$A.$ The surface energy per nucleon $(b_s) = a_1 A^{2/3}$
$B.$ The Coulomb contribution to the binding energy $b_c = -a_2 \frac{Z(Z-1)}{A^{4/3}}$
$C.$ The volume energy $b_v = a_3 A$
$D.$ Decrease in the binding energy is proportional to surface area.
$E.$ While estimating the surface energy,it is assumed that each nucleon interacts with $12$ nucleons,($a_1, a_2$ and $a_3$ are constants)
Choose the most appropriate answer from the options given below: