A neutron strikes a ${ }_{92} U ^{235}$ nucleus and as a result ${ }_{38} Kr ^{93}$ and ${ }_{56} Ba ^{140}$ are produced with

The $\beta$-decay process, discovered around $1900$ , is basically the decay of a neutron ( $n$ ), In the laboratory, a proton ( $p$ ) and an electron ( $e ^{-}$) are observed as the decay products of the neutron. therefore, considering the decay of a neutron as a tro-body dcay process, it was predicted theoretically that thekinetic energy of the electron should be a constant. But experimentally, it was observed that the electron kinetic energy has a continuous spectrum. Considering a three-body decay process, i.e. $n \rightarrow p+ e ^{-}+\bar{v}_{ e }$, around $1930,$ Pauli explained the observed electron energy spectrum. Assuming the anti-neutrino $\left(\bar{v}_{ e }\right)$ to be massless and possessing negligible energy, and neutron to be at rest, momentum and energy conservation principles are applied. From this calculation, the maximum kinetic energy of the lectron is $0.8 \times 10^6 eV$. The kinetic energy carried by the proton is only the recoil energy.

$1.$ What is the maximum energy of the anti-neutrino?

$(A)$ Zero

$(B)$ Much less than $0.8 \times 10^6 \ eV$

$(C)$ Nearly $0.8 \times 10^6 \ eV$

$(D)$ Much larger than $0.8 \times 10^6 \ eV$

$2.$ If the anti-neutrino had a mass of $3 eV / c ^2$ (where $c$ is the speed of light) instead of zero mass, what should be the range of the kinetic energy, $K$, of the electron?

$(A)$ $0 \leq K \leq 0.8 \times 10^6 \ eV$

$(B)$ $3.0 eV \leq K \leq 0.8 \times 10^6 \ eV$

$(C)$ $3.0 eV \leq K < 0.8 \times 10^6 \ eV$

$(D)$ $0 \leq K < 0.8 \times 10^6 \ eV$

Give the answer question $1$ and $2.$

Some laws/processes are given in Column $I$. Match these with the physical phenomena given in Column $II$ and indicate your answer by darkening appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.

Write nuclear reaction equations for

$(i)$ $\alpha$ -decay of $^{226}_{88} Ra$

$(ii)$ $\alpha$ -decay of $_{94}^{242} Pu$

$(iii)$ $\beta$ -decay of $_{15}^{32} P$

$(iv)$ $\beta$ -decay of $^{210}_{83}Bi$

$(v)$ $\beta^{+}$ -decay of $_{6}^{11} C$

$(vi)$ $\beta^{+}$ -decay of $_{43}^{97} Tc$

$(vii)$ Electron capture of $^{120}_{54} Xe$

The composition of an $\alpha $- particle can be expressed as

A plot of the number of neutrons $(N)$ against the number of protons ( $P$ )of stable nuclei exhibits upward deviation from linearity for atomic number, $Z>20$. For an unstable nucleus having $N / P$ ratio less than $1$ , the possible mode($s$) of decay is(are)

($A$) $\beta^{-}$-decay ( $\beta$ emission)

($B$) orbital or $K$-electron sasture

($C$) neutron emission

($D$) $\beta^{+}$-decay (positron emission)