Which one of the following combinations of radioactive decay results in the formation of an isotope of the original nucleus?

Options

A. One alpha and four beta
B. One alpha and two beta
C. One alpha and one beta
D. Two alpha and one beta

Answer

To solve the question "Which one of the following combinations of radioactive decay results in the formation of an isotope of the original nucleus?", we need to analyze each option based on the definitions of isotopes and the effects of different types of radioactive decay.

### Step-by-Step Solution:

1. **Understanding Isotopes**:
- Isotopes are nuclei that have the same atomic number (Z) but different mass numbers (A). Therefore, for a decay process to result in an isotope, the atomic number must remain unchanged while the mass number may change.

2. **Analyzing the Options**:
- We will analyze each option to see if the atomic number remains the same after the decay process.

3. **Option A: 1α and 4β**:
- An α particle (1α) is equivalent to a Helium nucleus (He²⁴), which decreases the atomic number by 2.
- A β particle (4β) represents 4 beta decays (each β decay increases the atomic number by 1).
- Total change in atomic number: Z - 2 (from α) + 4 (from β) = Z + 2.
- Result: Not an isotope (Z changes).

4. **Option B: 1α and 2β**:
- 1α decreases the atomic number by 2.
- 2β increases the atomic number by 2 (2 beta decays).
- Total change in atomic number: Z - 2 + 2 = Z.
- Result: The atomic number remains the same, hence it results in an isotope.

5. **Option C: 1α and 1β**:
- 1α decreases the atomic number by 2.
- 1β increases the atomic number by 1.
- Total change in atomic number: Z - 2 + 1 = Z - 1.
- Result: Not an isotope (Z changes).

6. **Option D: 2α and 1β**:
- 2α decreases the atomic number by 4.
- 1β increases the atomic number by 1.
- Total change in atomic number: Z - 4 + 1 = Z - 3.
- Result: Not an isotope (Z changes).

7. **Conclusion**:
- The only option that results in the formation of an isotope of the original nucleus is **Option B: 1α and 2β**.

### Final Answer:
**Option B: 1α and 2β results in the formation of an isotope of the original nucleus.**

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