Question

A nucleus \( _{Z}^A X \) emits an \( \alpha \)-particle. The resultant nucleus emits a \( \beta^- \)-particle. The respective atomic and mass numbers of the final nucleus will be:

• A. \( _{Z-2}^{A-4} \)
• B. \( _{Z-1}^{A-4} \)
• C. \( _{Z-2}^{A-2} \)
• D. \( _{Z-1}^{A-2} \)

Hint:

In nuclear reactions, the emission of an \( \alpha \)-particle decreases both the atomic and mass numbers, while a \( \beta^- \)-particle increases the atomic number.

Answer 1

The Correct Option is D

Step 1: Understand the decay process.
When a nucleus emits an \( \alpha \)-particle, the atomic number decreases by 2 and the mass number decreases by 4. Upon subsequent emission of a \( \beta^- \)-particle, the atomic number increases by 1 but the mass number remains unchanged.
Step 2: Conclusion.
Thus, the final atomic number is \( Z-1 \) and the mass number is \( A-2 \).
Final Answer: \[ \boxed{D} \]