Question

Explain with example whether the neutron to proton ratio increases or decreases due to $\beta -decay$ .

Answer 1

Neutron to proton ratio, as the name itself suggests, is the ratio of the number of neutrons to the number of protons in an atomic nucleus. So if we can find the changes in the nucleus caused due to $\beta -decay$, we can easily answer the question at hand.

Complete step by step answer:
$\beta -particle$is a high energy particle that resembles an electron. These particles are of two types: ${{\beta }^{-}}and{{\beta }^{+}}$. They are emitted from an atomic nucleus as a result of nuclear fission reaction in radioactive decay.
${{\beta }^{-}}$ is a high energy electron. It differs from the atomic electrons in the origin because they originate from the nucleus of the atom.
${{\beta }^{+}}$ are the high energy electrons with a positive charge.
$\beta -decay$ is the process in which a $\beta -particle$ is emitted from an atomic nucleus, in the process of nuclear fission, as a part of radioactive decay.
In an atomic nucleus, when the ratio of neutrons to protons is very high, that is when there are too many neutrons in an atom, excess neutrons transform into a proton and an electron.
Then the number of neutrons decreases and the number of protons increases simultaneously. The excess electron created is affected out of the nucleus of the atom. Thus, we can now say that, when $\beta -decay$ takes place, the number of protons increases and the number of neutrons decreases. Hence the neutron to proton ratio decreases.
We can use this example to gain a better understanding.
${}_{6}^{14}C\to {}_{7}^{14}N+{{e}^{-}}_{{}}$
In the above example, where the carbon atom has 6 protons and 8 neutrons have undergone radioactive decay and one neutron has got converted into a proton and an electron.
Thus, the number of neutrons has decreased from 8 to 7 and the number of protons has increased from 6 to 7.
The neutron-proton ratio of the carbon nucleus is, $\dfrac{8}{6}=\dfrac{4}{3}$
The neutron to proton ratio of the nitrogen nucleus is, $\dfrac{7}{7}=1$

Thus, the ratio decreases.

Note:
In the above example, the ratio of neutrons to protons has decreased but the mass number remained the same. Therefore, there is no change in the number of nucleons during $\beta -decay$, only the number of neutrons and protons change.