Question

The choice(s) that correctly identify radioisotopes (P, Q, R, S) shown in the following nuclear reaction is(are):
\[ ^{60}_{28}\text{Ni} + \alpha \;\; \longrightarrow \;\; P \; (\text{unstable}) \] \[ P \;\longrightarrow\; n + Q, \qquad P \;\longrightarrow\; 2n + R, \qquad P \;\longrightarrow\; p + n + S \]

• A. \(P = ^{64}_{30}\text{Zn}\)
• B. \(Q = ^{63}_{30}\text{Zn}\)
• C. \(R = ^{62}_{29}\text{Cu}\)
• D. \(S = ^{62}_{29}\text{Cu}\)

Hint:

In nuclear equations, conserve both mass number \(A\) and atomic number \(Z\) for each channel.
Neutron emission: \(A \downarrow 1\), \(Z\) unchanged. \; Proton emission: \(A \downarrow 1\), \(Z \downarrow 1\).
Use these bookkeeping rules to test each proposed isotope quickly.

Answer 1

The Correct Option is A, B, D

Step 1: Determine \(P\). Add mass and atomic numbers: \[ ^{60}_{28}\text{Ni} + ^{4}_{2}\text{He} \Rightarrow A=60+4=64,\; Z=28+2=30 \Rightarrow P=\,^{64}_{30}\text{Zn}. \] Thus (A) is correct.
Step 2: First decay channel (\(n+Q\)). Emission of one neutron keeps \(Z\) the same and reduces \(A\) by 1: \[ ^{64}_{30}\text{Zn} \rightarrow n + \,^{63}_{30}\text{Zn} (=Q). \] So (B) is correct.
Step 3: Second decay channel (\(2n+R\)). Emission of two neutrons keeps \(Z=30\) and reduces \(A\) to 62, hence \[ R = \,^{62}_{30}\text{Zn}, \] not \(^{62}_{29}\text{Cu}\). Therefore option (C) is false.
Step 4: Third decay channel (\(p+n+S\)). Emission of a proton and a neutron reduces \(A\) by 2 and \(Z\) by 1: \[ ^{64}_{30}\text{Zn} \rightarrow p + n + \,^{62}_{29}\text{Cu} (=S), \] so (D) is correct.