Question

A radioactive nucleus emits 3 $\alpha$-particles and 2 $\beta$-particles. The ratio of the initial atomic number to the final atomic number is:

• A. $\frac{Z}{Z-4}$
• B. $\frac{Z}{Z-8}$
• C. $\frac{Z}{Z-6}$
• D. $\frac{Z}{Z-2}$

Hint:

$\alpha = \text{He nucleus } (Z-2, A-4)$; $\beta = \text{Electron } (Z+1, A-0)$.

Answer 1

The Correct Option is A

Step 1: Concept
Each $\alpha$-emission reduces $Z$ by 2. Each $\beta$-emission increases $Z$ by 1.
Step 2: Analysis
Total change in $Z = (3 \times -2) + (2 \times +1) = -6 + 2 = -4$.
Final atomic number $Z' = Z - 4$.
Step 3: Conclusion
The ratio is $Z / (Z - 4)$.
Final Answer: (A)