A free neutron decays to a proton but a free proton does not decay to a neutron. This is because — Nuclear Chemistry and Radioactivity Chemistry Question

💡 Solution & Explanation

Step 1 - Condition for Spontaneous Decay For any spontaneous decay $X \to Y_1 + Y_2 + \ldots$, conservation of mass-energy requires: $$m_{\text{parent}} > \sum m_{\text{products}}$$ If $m_{\text{parent}} < \sum m_{\text{products}}$, the process cannot occur spontaneously. Step 2 - Free Neutron Decay A free neutron undergoes $\beta^-$ decay: $$\ce{n -> p + e^- + \bar{\nu}_e}$$ Mass check: - $m_n \approx 1.6749 \times 10^{-27}$ kg - $m_p + m_e \approx 1.6726 \times 10^{-27} + 0.00091 \times 10^{-27} = 1.6735 \times 10^{-27}$ kg Since $m_n > m_p + m_e$, the decay is energetically favored. ✓ Step 3 - Free Proton Cannot Decay to Neutron The hypothetical proton decay: $$\ce{p -> n + e^+ + \nu_e}$$ Mass check: - $m_p \approx 1.6726 \times 10^{-27}$ kg - $m_n + m_{e^+} \approx 1.6749 \times 10^{-27} + 0.00091 \times 10^{-27} = 1.6758 \times 10^{-27}$ kg Since $m_p < m_n + m_{e^+}$, this process requires external energy — it cannot occur spontaneously. Step 4 - Evaluate Options - **(A)** Incorrect. Both protons and neutrons are composite quark particles ($uud$ and $udd$), not fundamental. - **(B)** Incorrect. Charge status is conserved in all decays but does not determine spontaneity. - **(C)** Correct. $m_n > m_p$, so the neutron has enough mass-energy to decay; the proton does not. - **(D)** Incorrect. Weak nuclear force operates inside both protons and neutrons (quark flavor changes). $$\boxed{\text{Answer: C}}$$