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

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.