Discussion
Match the order of β-decays given in the left column to appropriate clause in the right column. Here \(X(I^{\pi})\) and \(Y(I^{\pi})\) are nuclei with intrinsic spin \(I\) and parity \(\pi\).
| 1. \(X\left(\frac{1}{2}^{+}\right) \rightarrow Y\left(\frac{1}{2}^{+}\right)\) | i) First forbidden β-decay |
| 2. \(X\left(\frac{1}{2}^{-}\right) \rightarrow Y\left(\frac{5}{2}^{+}\right)\) | ii) Second forbidden β-decay |
| 3. \(X(3^{+}) \rightarrow Y(0^{+})\) | iii) Third forbidden β-decay |
| 4. \(X(4^{-}) \rightarrow Y(0^{+})\) | iv) Allowed β-decay |
Answer: B
The match is 1-iv, 2-i, 3-ii, 4-iii.
The order of forbiddenness is set by the spin change \(\Delta I\) and whether the parity changes. Allowed decays have \(\Delta I = 0, 1\) and no parity change. A forbidden decay of order \(n\) needs \(n\) units of orbital angular momentum, with parity change for odd \(n\); a unique transition has \(\Delta I = n + 1\).
- 1: \(\frac{1}{2}^{+} \to \frac{1}{2}^{+}\), \(\Delta I = 0\), no parity change: allowed.
- 2: \(\frac{1}{2}^{-} \to \frac{5}{2}^{+}\), \(\Delta I = 2\), parity changes: first forbidden (unique).
- 3: \(3^{+} \to 0^{+}\), \(\Delta I = 3\), no parity change: second forbidden (unique).
- 4: \(4^{-} \to 0^{+}\), \(\Delta I = 4\), parity changes: third forbidden (unique).
The other options misplace the allowed decay or reverse the order of the forbidden ones.
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