JEE Main 2023 · 31 January · morning · Single correct · +4 / −1
A free neutron decays into a proton but a free proton does not decay into neutron. This is because
- (a) neutron is an uncharged particle
- (b) neutron has larger rest mass than proton
- (c) neutron is a composite particle made of a proton and an electron
- (d) proton is a charged particle
Answer and solution
Answer (b) neutron has larger rest mass than proton
Solution
Physics sir · 4 steps
A free particle can only decay downhill in mass: the neutron is heavier, so only it can turn into a proton.
- Rule for decay. A free particle at rest can decay only if its rest-mass energy is larger than the total rest-mass energy of the products. The extra mass becomes the kinetic energy of the products, called the Q-value.
- Neutron decay. n → p + e⁻ + ν̄. With mₙ c² = 939.565 MeV, mₚ c² = 938.272 MeV and mₑ c² = 0.511 MeV, the Q-value is positive, so this decay happens.
Q = (mₙ - mₚ - mₑ)c² = 939.565 - 938.272 - 0.511 = +0.782 MeV
- Proton decay. For p → n + e⁺ + ν, Q = 938.272 - 939.565 - 0.511 = -1.804 MeV. A free proton has no outside source for this missing energy, so it cannot decay.
- So. The deciding fact is that the neutron has a larger rest mass than the proton, which is option (b).
The idea to keep. To check whether a free particle can decay, compare masses. Products must weigh less than the parent. Inside a nucleus, binding energy can make up the shortfall, which is why β⁺ decay is possible there.
Answer from the NTA final answer key. Solution by PrepWiser.