Which of the following element is an isodiapher of `._(92)U^(235)`?

Options

A. a`._(82)Pb^(212)`
B. b. `._(90)Th^(231)`
C. c. `._(83)Bi^(209)`
D. d. `._(91)Pa^(231)`

Explanation

To determine which element is an isodiapher of Uranium-235 \((^{235}_{92}U)\), we need to understand the concept of isodiaphers. Isodiaphers are nuclides that have the same difference between the number of protons and neutrons (i.e., the same value of \(N - Z\), where \(N\) is the number of neutrons and \(Z\) is the number of protons).

### Step-by-Step Solution:

1. **Identify the Atomic Number and Mass Number of Uranium-235**:
- Uranium-235 has an atomic number \(Z = 92\) and a mass number \(A = 235\).

2. **Calculate the Number of Neutrons in Uranium-235**:
- The number of neutrons \(N\) can be calculated using the formula:
\[ N = A - Z = 235 - 92 = 143 \]

3. **Determine the Value of \(N - Z\)**:
- Now, we find \(N - Z\):
\[ N - Z = 143 - 92 = 51 \]

4. **Identify the Isodiapher**:
- An isodiapher will have the same \(N - Z\) value of 51. We need to find an element with \(N - Z = 51\) and check if it is formed from Uranium-235 through alpha decay.

5. **Consider Alpha Decay**:
- In alpha decay, an element emits an alpha particle \((^{4}_{2}He)\), which decreases the mass number by 4 and the atomic number by 2.
- The new element after alpha decay from Uranium-235 will have:
- New mass number \(A' = 235 - 4 = 231\)
- New atomic number \(Z' = 92 - 2 = 90\)

6. **Identify the New Element**:
- The new element with atomic number 90 is Thorium \((^{231}_{90}Th)\).

7. **Confirm the Neutron Count for Thorium-231**:
- Calculate the number of neutrons in Thorium-231:
\[ N' = A' - Z' = 231 - 90 = 141 \]
- Now check \(N' - Z'\):
\[ N' - Z' = 141 - 90 = 51 \]

8. **Conclusion**:
- Since Thorium-231 has the same \(N - Z\) value of 51, it is an isodiapher of Uranium-235.

### Final Answer:
The isodiapher of Uranium-235 \((^{235}_{92}U)\) is Thorium-231 \((^{231}_{90}Th)\).