In the given reaction `._(92)U^(235) overset(-alpha)rarr (A) overset(-beta)rarr (B) overset(-beta)rarr (C)` isotopes are

Options

A. A and C
B. `._(92)U^(235)` and C
C. A and B
D. A, B and C

Explanation

To solve the problem, we need to analyze the given nuclear reactions step by step, starting from Uranium-235 and tracking the changes in atomic number and mass number through the decay processes.

### Step 1: Identify the initial isotope
The initial isotope is Uranium-235, denoted as \( _{92}^{235}U \).

### Step 2: Alpha decay
In the first step, Uranium-235 undergoes alpha decay. An alpha particle (which consists of 2 protons and 2 neutrons) is emitted.

- **Mass number change**: The mass number decreases by 4 (235 - 4 = 231).
- **Atomic number change**: The atomic number decreases by 2 (92 - 2 = 90).

Thus, the resulting isotope \( A \) is:
\[ A = _{90}^{231}Th \quad (\text{Thorium-231}) \]

### Step 3: First beta decay
Next, isotope \( A \) undergoes beta decay. In beta decay, a neutron is converted into a proton, and a beta particle (an electron) is emitted.

- **Mass number change**: The mass number remains the same (231).
- **Atomic number change**: The atomic number increases by 1 (90 + 1 = 91).

Thus, the resulting isotope \( B \) is:
\[ B = _{91}^{231}Pa \quad (\text{Protactinium-231}) \]

### Step 4: Second beta decay
Finally, isotope \( B \) undergoes another beta decay.

- **Mass number change**: The mass number remains the same (231).
- **Atomic number change**: The atomic number increases by 1 (91 + 1 = 92).

Thus, the resulting isotope \( C \) is:
\[ C = _{92}^{231}U \quad (\text{Uranium-231}) \]

### Summary of isotopes
- Initial isotope: \( _{92}^{235}U \) (Uranium-235)
- After alpha decay: \( _{90}^{231}Th \) (Thorium-231)
- After first beta decay: \( _{91}^{231}Pa \) (Protactinium-231)
- After second beta decay: \( _{92}^{231}U \) (Uranium-231)

### Conclusion
The isotopes involved in the reaction are:
1. Uranium-235
2. Thorium-231
3. Protactinium-231
4. Uranium-231

### Final Answer
The isotopes are \( _{92}^{235}U \) (Uranium-235) and \( _{92}^{231}U \) (Uranium-231), which are isotopes of Uranium.

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