The rest mass of the deuteron,${}_1^2H$,is equivalent to an energy of $1876 \, MeV$. The rest mass of a proton is equivalent to $939 \, MeV$ and that of a neutron is $940 \, MeV$. $A$ deuteron may disintegrate into a proton and a neutron if it:

  • A
    emits a $\gamma$-ray photon of energy $2 \, MeV$
  • B
    captures a $\gamma$-ray photon of energy $2 \, MeV$
  • C
    emits a $\gamma$-ray photon of energy $3 \, MeV$
  • D
    captures a $\gamma$-ray photon of energy $3 \, MeV$

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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

If the binding energy per nucleon for $_3{Li}^7$ and $_2{He}^4$ nuclei are $5.60 \, MeV$ and $7.06 \, MeV$ respectively,then the energy released in the reaction $_3{Li}^7 + _1H^1 \rightarrow 2 \, _2{He}^4$ is ...... $MeV$.

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$A$ nucleus $^{A}_{Z} X$ has mass represented by $M(A, Z)$. If $M_p$ and $M_n$ denote the mass of a proton and a neutron respectively, and $B.E.$ is the binding energy in $MeV$, then:

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

The neutron separation energy is defined as the energy required to remove a neutron from the nucleus. Obtain the neutron separation energies of the nuclei $_{20}^{41} Ca$ and $_{13}^{27} Al$ from the following data:
$m(_{20}^{40} Ca) = 39.962591 \; u$
$m(_{20}^{41} Ca) = 40.962278 \; u$
$m(_{13}^{26} Al) = 25.986895 \; u$
$m(_{13}^{27} Al) = 26.981541 \; u$
(Given mass of neutron $m_n = 1.008665 \; u$)

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