JEE Physics 2023 Question with Solution

Given: A free neutron decays into a proton, but a free proton does not decay into a neutron.

Find: The correct reason for this behavior.

Free neutron undergoes beta decay:

$$n \rightarrow p + e^- + \bar{\nu}_e$$

This decay is possible only if the initial particle has greater rest mass than the total rest mass of the products.

The solution states that the neutron's mass is slightly greater than that of the proton, so neutron decay is energetically allowed. In contrast, a free proton cannot decay into a neutron because that process would require additional energy and is therefore not energetically favorable.

Therefore, the correct option is B according to the solution, although the option text corresponding to the physical reason is "Neutron has larger rest mass than proton".

Given: A neutron decays spontaneously, but a free proton does not.

Find: Which statement explains this.

The key principle is mass-energy conservation. A spontaneous decay can occur only when the parent particle has enough rest mass energy.

For neutron decay:

$$n \rightarrow p + e^- + \bar{\nu}_e$$

Since the neutron has slightly larger rest mass than the proton, the decay can proceed.

For proton to turn into neutron spontaneously, the proton would need to produce a heavier particle, which is not possible without external energy.

Thus, the physical conclusion is that neutron decay occurs because the neutron has larger rest mass than the proton. The solution marks option B, but this corresponds to a mismatch with the listed options. The defensible choice from the provided options is the statement about larger neutron rest mass.