Question

A nucleus decays by \[\beta + - \;\] emission followed by a \[\gamma - \]emission. If the atomic and mass numbers of the parent nucleus are \[Z\] and \[A\]respectively, the corresponding numbers for the daughter nucleus are
A. \[Z - 1\] and \[A - 1\]
B. \[Z + 1\] and \[A\]
C. \[Z - 1\] and \[A\]
D. \[Z + 1\] and \[A - 1\]

Answer 1

Hint: In the given question, we need to find the corresponding numbers for the daughter nucleus for \[\beta + - \;\]emission and a \[\gamma - \]emission respectively. For this, we have to explain alpha particles and beta decay. Also, we will give an explanation about the new atomic number and mass number.

Complete step by step solution:
We know that \[\beta - \] rays are considered as fast moving electrons. Also, whenever there is an excess amount of proton present in the nucleus and also it is impossible to emit an \[\alpha - \] particle, thus \[\beta + \]decay occurs. As a result, the atomic number is decreased by one unit. Mathematically, it is given by \[Z - 1\].

In this case, the mass number is unchanged. So, the gamma ray emission occurs with \[p4\] emission. Their emission does not change the chemical composition of the atom as the gamma rays have no charge or mass. Hence, their atomic number and mass number are \[Z - 1\] and \[A\] respectively. So, during \[\beta + \] decay, a positron and a neutrino are also released.

Thus, a nucleus decays by \[\beta + \;\] emission followed by a \[\gamma - \] emission. If the atomic and mass numbers of the parent nucleus are \[Z\] and \[A\] respectively, the corresponding numbers for the daughter nucleus are \[Z - 1\] and \[A\] respectively.

Therefore, the correct option is C.

Note:Many students may make mistakes in writing the explanation part such as they forget to write about no emission of alpha particles. It is necessary to explain all three types of emission such as alpha, beta and gamma.