Discussion
As per the nuclear stability rule, the following nuclear decay :
\(^{5}_{3}\text{Li} \rightarrow {}^{4}_{2}\text{He} + \text{P}\)
can be possible because :
Answer: C
The decay is possible because the mass of \(^{5}\)Li is greater than the sum of the masses of \(^{4}\)He and P.
A spontaneous decay can occur only if it releases energy, that is if the Q-value is positive:
\[ \begin{aligned} Q &= [M(^{5}\text{Li}) - M(^{4}\text{He}) \\ &\quad - M_{p}]c^{2} \gt 0 \end{aligned} \]
Lithium-5 is indeed unbound: it falls apart into an alpha particle and a proton almost instantly, with a Q-value of about 2 MeV. If its mass were smaller than the products' mass, the decay would be energetically forbidden. Spin decides which angular momenta the products may carry away, not whether the decay is possible, so the options about spin are wrong.
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