For the given reaction, \(n \rightarrow p + \pi^{-}\), which of the conservation statements is true?
All conservations hold true, the reaction is allowed
Baryon number: \(B(n) = 1\); \(B(p) + B(\pi^{-}) = 1 + 0 = 1\). Conserved.
Electric charge: \(Q(n) = 0\); \(Q(p) + Q(\pi^{-}) = (+1) + (-1) = 0\). Conserved.
Electron lepton number: no leptons on either side, \(L_{e} = 0\) on both sides. Conserved.
All the listed additive quantum numbers are conserved, so the process is allowed by the conservation laws in question (the free neutron mass is however below \(m_p + m_{\pi}\), so it is kinematically forbidden for a free neutron, but the conservation statements themselves hold).
Hence, all conservations hold true and the reaction is allowed by these conservation laws.
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