Consider the following two hypothetical nuclear processes for free particles at rest: Reaction I: n p + e⁻ + _ e with an energy release of Q₁ Reaction II: p n + e⁺ + _ e with an energy release of Q₂ It is observed that a free neutron decays spontaneously, whereas a free proton is stable. Which of the following correctly represents the conditions for Q₁ and Q₂ ?

Step-by-step solution

For any nuclear process to occur spontaneously in free space, the Q -value of the reaction must be positive ( Q > 0 ). This implies that the total rest mass of the initial particles must be greater than the total rest mass of the final particles. The rest mass of a neutron is greater than the combined rest mass of a proton and an electron. Thus, for Reaction I, the mass defect is positive, leading to Q₁ > 0 . This allows the free neutron to decay spontaneously. Conversely, the rest mass of a proton is less than tha