$A$ nucleus of mass $M + \Delta m$ is at rest and decays into two daughter nuclei of equal mass. If $C$ is the speed of light,and $E_1$ is the binding energy per nucleon for the parent nucleus and $E_2$ is that for the daughter nuclei,then:

If $m$ is the mass of the $_Z{X^A}$ nucleus,and $m_n$ and $m_p$ are the masses of a neutron and a proton respectively,then which of the following is correct?

If the binding energy per nucleon for $\,_3^7\,Li\,\,$ and $\,_2^4\,\,He$ are $5.60 \,MeV$ and $7.06 \,MeV$ respectively, then the energy of the proton in the reaction $p\,\, + \,\,_3^7\,\,Li\,\, \to \,\,2\,_2^4\,\,He$ must be .......... $MeV$.

The binding energy per nucleon of $^{209}_{83}Bi$ is . . . . . . MeV. [Take $m(^{209}_{83}Bi) = 208.980388 \text{ u}$, $m_p = 1.007825 \text{ u}$, $m_n = 1.008665 \text{ u}$, $1 \text{ u} = 931 \text{ MeV}/c^2$]

$A$ nucleus of mass $M + \Delta m$ is at rest and decays into two daughter nuclei of equal mass $\frac{M}{2}$ each. The speed of light is $c$. The binding energy per nucleon for the parent nucleus is $E_1$ and that for the daughter nuclei is $E_2$. Then:

Given the masses of various atomic particles $m_{p} = 1.0072 \ u$,$m_{n} = 1.0087 \ u$,$m_{e} = 0.000548 \ u$,$m_{\bar{v}} = 0$,and $m_{d} = 2.0141 \ u$,where $p \equiv$ proton,$n \equiv$ neutron,$e \equiv$ electron,$\bar{v} \equiv$ antineutrino,and $d \equiv$ deuteron. Which of the following processes is allowed by momentum and energy conservation?