The figure shows a plot of binding energy per nucleon $E_b$ against the nuclear mass $M$. $A, B, C, D, E, F$ correspond to different nuclei. Consider four reactions:
$(i) \, A + B \to C + \varepsilon$
$(ii) \, C \to A + B + \varepsilon$
$(iii) \, D + E \to F + \varepsilon$
$(iv) \, F \to D + E + \varepsilon$
where $\varepsilon$ is the energy released. In which reactions is $\varepsilon$ positive?

  • A
    $(ii)$ and $(iv)$
  • B
    $(ii)$ and $(iii)$
  • C
    $(i)$ and $(iv)$
  • D
    $(i)$ and $(iii)$

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The mass equivalent of $931\, MeV$ energy is

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 $\qquad \text{ MeV}$.

$A$ plot of the number of neutrons $(N)$ against the number of protons $(Z)$ for stable nuclei exhibits upward deviation from linearity for atomic number $Z > 20$. For an unstable nucleus having an $N/Z$ ratio less than $1$,the possible mode$(s)$ of decay is(are):
$(A)$ $\beta^{-}$-decay ($\beta$ emission)
$(B)$ Orbital or $K$-electron capture
$(C)$ Neutron emission
$(D)$ $\beta^{+}$-decay (positron emission)

If $M(A, Z)$,$M_p$,and $M_n$ denote the masses of the nucleus ${}_Z^AX$,proton,and neutron respectively in units of $u$ $(1u = 931.5 \text{ MeV}/c^2)$,and $BE$ represents its binding energy in $\text{MeV}$,then:

The binding energy for the following nuclear reactions are expressed in $MeV$.
${ }_2 He ^3+{ }_0 n ^1 \rightarrow{ }_2 He ^4+20 \ MeV$
${ }_2 He ^4+{ }_0 n ^1 \rightarrow{ }_2 He ^5-0.9 \ MeV$
If $X_3, X_4, X_5$ denote the stability of ${ }_2 He ^3, { }_2 He ^4$ and ${ }_2 He ^5$, respectively, then the correct order is:

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