In the given reaction, `U_92^235overset(-alpha)to (A) overset(-beta)to(B) overset(-beta)to ©` isotope are :

Options

A. A and C
B. `U_92^235`
C. A and B
D. A, B and C

Answer

To solve the problem step by step, we will analyze the decay process of Uranium-235 (U-235) and determine the isotopes formed at each stage.

### Step 1: Identify the initial isotope
The initial isotope is Uranium-235, represented as:
\[ U_{92}^{235} \]

### Step 2: Alpha decay of U-235
In alpha decay, an alpha particle (which consists of 2 protons and 2 neutrons) is emitted. This results in:
- The mass number decreases by 4 (because of the 4 nucleons in the alpha particle).
- The atomic number decreases by 2 (because of the 2 protons in the alpha particle).

Calculating the new isotope:
- New mass number = 235 - 4 = 231
- New atomic number = 92 - 2 = 90

Thus, after alpha decay, the new isotope A is:
\[ A_{90}^{231} \]

### Step 3: Beta decay of A
In beta decay, a neutron is converted into a proton, and a beta particle (an electron) is emitted. This results in:
- The mass number remains the same.
- The atomic number increases by 1.

Calculating the new isotope:
- New mass number = 231 (remains the same)
- New atomic number = 90 + 1 = 91

Thus, after the first beta decay, the new isotope B is:
\[ B_{91}^{231} \]

### Step 4: Beta decay of B
B undergoes another beta decay, which again results in:
- The mass number remains the same.
- The atomic number increases by 1.

Calculating the new isotope:
- New mass number = 231 (remains the same)
- New atomic number = 91 + 1 = 92

Thus, after the second beta decay, the new isotope C is:
\[ C_{92}^{231} \]

### Step 5: Identify isotopes
Isotopes are defined as atoms of the same element (same atomic number) that have different mass numbers.

From our calculations:
- U-235 has atomic number 92 and mass number 235.
- C has atomic number 92 and mass number 231.

Thus, the isotopes are:
1. U-235 (Uranium-235)
2. C-231 (Uranium-231)

### Final Answer
The isotopes are:
- \( U_{92}^{235} \) (Uranium-235)
- \( C_{92}^{231} \) (Uranium-231)

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