JEE Main 2021 · 18 March · evening · Single correct · +4 / −1
The decay of a proton to neutron is :
- (a) always possible as it is associated only with β⁺ decay
- (b) possible only inside the nucleus
- (c) not possible as proton mass is less than the neutron mass
- (d) not possible but neutron to proton conversation is possible
Answer and solution
Answer (b) possible only inside the nucleus
Solution
Physics sir · 4 steps
A free proton is lighter than a neutron, so it needs energy to convert, and only a nucleus can supply it.
- The reaction. A proton turns into a neutron in β⁺ decay, giving out a positron and a neutrino.
p → n + e⁺ + ν
- Free proton. The neutron is heavier than the proton by about 1.29 MeV, and the positron adds another 0.511 MeV. The products weigh more than the proton, so a free proton cannot decay this way. Energy would not be conserved.
- Inside a nucleus. In a proton-rich nucleus, the extra energy comes from the nucleus itself. After the conversion, the new nucleus is more tightly bound, and the gain in binding energy covers the missing mass. This is why β⁺ emitters exist.
- So. Proton to neutron conversion happens only inside the nucleus, which is option (b).
The idea to keep. A decay that goes uphill in mass can still happen inside a nucleus, because binding energy pays for it. Free neutrons decay to protons, but free protons never decay to neutrons.
Answer from the NTA final answer key. Solution by PrepWiser.