The binding energy per nucleon of a nucleus ${}_Z X^A$ at rest is $6 \ MeV$. It undergoes $\beta^-$ decay as shown below:
${}_Z X^A \to {}_{Z+1} Y^A + {}_{-1}^0 e + \bar{\nu}$
The total kinetic energy $(K.E.)$ of the products is $3 \ MeV$. The binding energy per nucleon of $Y$ (in $MeV$) is:

Assertion : The binding energy per nucleon,for nuclei with atomic mass number $A > 100$,decreases with $A$.
Reason : The nuclear forces are weak for heavier nuclei.

The graph shows the binding energy per nucleon versus mass number. $A, B, C, D, E, F$ are different nuclei. Four processes are given where $\varepsilon$ is the energy released. In which process is $\varepsilon > 0$?
$(i) \, A + B \rightarrow C + \varepsilon$
$(ii) \, C \rightarrow A + B + \varepsilon$
$(iii) \, D + E \rightarrow F + \varepsilon$
$(iv) \, F \rightarrow D + E + \varepsilon$

List-$I$ shows various functional dependencies of energy $(E)$ on the atomic number $(Z)$. Energies associated with certain phenomena are given in List-$II$. Choose the option that describes the correct match between the entries in List-$I$ to those in List-$II$.

List-$I$	List-$II$
$(P) \ E \propto Z^2$	$(1)$ energy of characteristic $x-$rays
$(Q) \ E \propto (Z-1)^2$	$(2)$ electrostatic part of the nuclear binding energy for stable nuclei with mass numbers in the range $30$ to $170$
$(R) \ E \propto Z(Z-1)$	$(3)$ energy of continuous $x-$rays
$(S) \ E$ is practically independent of $Z$	$(4)$ average nuclear binding energy per nucleon for stable nuclei with mass number in the range $30$ to $170$
	$(5)$ energy of radiation due to electronic transitions from hydrogen-like atoms

The mass defect for the nucleus of helium is $0.0303 \, a.m.u.$ What is the binding energy per nucleon for helium in $MeV$?

One atomic mass unit is equivalent to .............. $MeV$ energy.