For explaining $\beta $-decay, which conservation law in the neutrino hypothesis is useful?

Hint:We know that the spontaneous breakdown of an atomic nucleus is known as the radioactive decay. The radioactive decay in which a beta ray is emitted from an atomic nucleus is called the Beta-decay. To answer this question, we need to understand the concept of $\beta $ -decay.

Complete answer:
In the process of beta decay, the proton in the nucleus is transformed into a neutron and vice versa. If a proton is converted to a neutron, it is known as $\beta + $ decay. Similarly, if a neutron is converted to a proton, it is known as $\beta $- decay. Due to the change in the nucleus, a beta particle is emitted. The beta particle is a high-speed electron when it is a $\beta $- decay and a positron when it is a $\beta + $ decay.
Here, we have seen that in this process, only the proton in the nucleus is transformed into a neutron and vice versa and the total energy remains constant. Thus, we can say that for explaining $\beta $-decay, energy conservation law in the neutrino hypothesis is useful.

Note:Here, we have seen that the energy conservation law in the neutrino hypothesis is useful for explaining beta decay. We can understand this by the beta decay of carbon atoms. In this decay, a neutron of carbon is converted into a proton and the emitted beta particle is an electron. Thus, there is no energy transfer in this decay and thus the energy is conserved.