A radioactive nucleus ${}_{Z}^{A}\mathrm{X}$ undergoes spontaneous decay in the sequence ${}_{Z}\mathrm{X} \ri

Question

A radioactive nucleus ${}_{Z}^{A}\mathrm{X}$ undergoes spontaneous decay in the sequence ${}_{Z}\mathrm{X} \rightarrow {}_{Z-1}\mathrm{B} \rightarrow {}_{Z-3}\mathrm{C} \rightarrow {}_{Z-2}\mathrm{D}$, where $Z$ is the atomic number of element $\mathrm{X}$. The possible decay particles in the sequence are:

Accepted Answer

1. **Analyze Step 1 ($X_Z \rightarrow B_{Z-1}$):** The atomic number decreases by 1 ($Z \rightarrow Z-1$). This change is characteristic of **$\beta^+$ decay** (positron emission), where a proton converts into a neutron, reducing the nuclear charge by 1 unit .
2. **Analyze Step 2 ($B_{Z-1} \rightarrow C_{Z-3}$):** The atomic number decreases by 2 (from $Z-1$ to $Z-3$). This change corresponds to **$\alpha$ decay**, where an alpha particle (${}_{2}^{4}\mathrm{He}$) is emitted, reducing the atomic number by 2 .
3. **Analyze Step 3 ($C_{Z-3} \rightarrow D_{Z-2}$):** The atomic number increases by 1 (from $Z-3$ to $Z-2$). This change is characteristic of **$\beta^-$ decay** (electron emission), where a neutron converts into a proton, increasing the nuclear charge by 1 unit .
4. **Conclusion:** The sequence of particles emitted is $\beta^+, \alpha, \beta^-$.

Step-by-Step Solution

Practice All PHYSICS Questions