Radioactivity — Question 15

(a) If the nucleus X of a radioactive element of mass number A and atomic number Z emits an α particle, the daughter nucleus Y of a new element has mass number equal to (A - 4) and atomic number equal to (Z - 2).
Thus, atomic number decreases by 2 units and mass number decreases by 4 units.

$\begin{matrix} _{Z}^{A}\text{X} & \longrightarrow & _{Z-2}^{A-4}\text{Y} & + & \space _{2}^{4}\text{He} \\ \footnotesize{\text{Parent nucleus}} & & \footnotesize{\text{Daughter nucleus}} & & \footnotesize{\text{(α-particle)}} \end{matrix}$

Example — When a radioactive uranium nucleus $_{92}^{238}\text{U}$ emits an α particle, a new nucleus thorium $_{90}^{234}\text{Th}$ is formed and the change is represented as follows —

$_{92}^{238}\text{U} \longrightarrow \space _{90}^{234}\text{Th} + \space _{2}^{4}\text{He}$

(b) In emitting a β particle, the number of nucleons in the nucleus remains same, but the number of neutrons is decreased by one and the number of protons is increased by one.
If a radioactive nucleus P with mass number A and atomic number Z emits a β particle to form a daughter nucleus Q with mass number A and atomic number Z + 1, the change can be represented as follows:

$\begin{matrix} _{Z}^{A}\text{P} & \longrightarrow & _{Z+1}^{\space \space \space \space \space A}\text{Q} & + & \space _{-1}^{\space \space \space 0}\text{e} \\ \footnotesize{\text{Parent nucleus}} & & \footnotesize{\text{Daughter nucleus}} & & \footnotesize{\text{(β-particle)}} \end{matrix}$

Example — A radioactive carbon nucleus $_{6}^{14}\text{C}$, having 14 nucleons (6 protons and 8 neutrons) emits a β particle and changes to a new nucleus nitrogen $_{7}^{14}\text{N}$ having 14 nucleons (7 protons and 7 neutrons).

The change is represented as follows —

$_{6}^{14}\text{C} \longrightarrow \space _{\space \space 7}^{14}\text{N} + _{-1}^{\space \space \space 0}\text{e}$

(c) There is no change in the mass number A and atomic number Z of the nucleus in gamma emission. It is represented as follows:

$\begin{matrix} _{Z}^{A}\text{X*} & \longrightarrow & _{Z}^{A}\text{X} & + & \space \text{γ} \\ \footnotesize{\text{Parent nucleus}} & & \footnotesize{\text{Daughter nucleus}} & & \footnotesize{\text{(gamma radiation)}} \end{matrix}$

Here the star indicates the excited state of the nucleus. Thus in gamma emission, the excited nucleus comes to its ground state.