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

Options

A. One alpha, four beta
B. One alpha, two beta
C. One alpha, one beta
D. Four alpha, one beta

Answer

To solve the question regarding which combination of radioactive decay results in the formation of an isotope of the original nucleus, we will follow these steps:

### Step 1: Understand the Definitions
- **Isotopes**: Isotopes are variants of a particular chemical element that have the same number of protons (atomic number, Z) but different numbers of neutrons (mass number, A). This means that isotopes of an element have the same Z but different A.

### Step 2: Identify the Types of Radioactive Decay
- The two common types of radioactive decay we will consider are:
- **Alpha Decay**: In this process, an alpha particle (which consists of 2 protons and 2 neutrons) is emitted from the nucleus. This results in a decrease of the atomic number (Z) by 2 and the mass number (A) by 4.
- **Beta Decay**: In this process, a neutron is converted into a proton, and a beta particle (an electron) is emitted. This results in an increase of the atomic number (Z) by 1 while the mass number (A) remains unchanged.

### Step 3: Analyze the Decay Combinations
- Let's consider a hypothetical nucleus represented as \( ^A_ZS \).
- If it undergoes **alpha decay**, it transforms to \( ^{A-4}_{Z-2}R \).
- If it then undergoes **beta decay**, it transforms to \( ^{A-4}_{Z-1}T \).

### Step 4: Check for Isotope Formation
- After the alpha decay, the new element has mass number \( A-4 \) and atomic number \( Z-2 \).
- After the beta decay, the atomic number increases by 1, resulting in \( Z-1 \) but the mass number remains \( A-4 \).
- To check if we can return to an isotope of the original nucleus, we need to ensure that the new nucleus has the same atomic number (Z) but a different mass number (A).

### Step 5: Conclusion
- The combination of alpha decay followed by beta decay results in a nucleus with the same mass number as the original nucleus (if we can adjust the decay processes accordingly), thus forming an isotope of the original nucleus.

### Final Answer
The combination of **alpha decay followed by beta decay** results in the formation of an isotope of the original nucleus.

---