Among the given elements, number of species which are isodiaphers of each other are____ `""_(92)U^(238), ""_(88)Ra^(230), ""_(89)Ac^(232),""_(Th)^(234)`.

Answer

To determine the number of species that are isodiaphers among the given elements, we need to understand the definition of isodiaphers. Isodiaphers are nuclides that have the same difference between the number of neutrons and protons, but different atomic numbers and mass numbers.

Let's analyze the given elements one by one:

1. **Uranium-238 (U-238)**:
- Atomic number (Z) = 92 (number of protons)
- Mass number (A) = 238 (number of protons + number of neutrons)
- Number of neutrons (N) = A - Z = 238 - 92 = 146
- Difference (N - Z) = 146 - 92 = 54

2. **Radium-230 (Ra-230)**:
- Atomic number (Z) = 88
- Mass number (A) = 230
- Number of neutrons (N) = A - Z = 230 - 88 = 142
- Difference (N - Z) = 142 - 88 = 54

3. **Actinium-232 (Ac-232)**:
- Atomic number (Z) = 89
- Mass number (A) = 232
- Number of neutrons (N) = A - Z = 232 - 89 = 143
- Difference (N - Z) = 143 - 89 = 54

4. **Thorium-234 (Th-234)**:
- Atomic number (Z) = 90
- Mass number (A) = 234
- Number of neutrons (N) = A - Z = 234 - 90 = 144
- Difference (N - Z) = 144 - 90 = 54

Now, we can summarize the differences calculated:
- U-238: Difference = 54
- Ra-230: Difference = 54
- Ac-232: Difference = 54
- Th-234: Difference = 54

All four species have the same difference (54) between the number of neutrons and protons, which means they are isodiaphers of each other.

**Final Answer**: The number of species which are isodiaphers of each other is **4**.