From the following nuclei select the isotopes and isobars :
`""_(92)^(238)U, ""_(90)^(234)Th, ""_(92)^(234)U, ""_(91)^(234)Pa` .

Answer

To determine the isotopes and isobars from the given nuclei, we need to understand the definitions:

1. **Isotopes**: Isotopes are nuclei that have the same atomic number (same number of protons) but different mass numbers (different number of neutrons).
2. **Isobars**: Isobars are nuclei that have the same mass number (same total number of protons and neutrons) but different atomic numbers (different number of protons).

Now, let's analyze the given nuclei:

1. **Uranium-238**: \( _{92}^{238}U \)
- Atomic Number (Z) = 92
- Mass Number (A) = 238

2. **Thorium-234**: \( _{90}^{234}Th \)
- Atomic Number (Z) = 90
- Mass Number (A) = 234

3. **Uranium-234**: \( _{92}^{234}U \)
- Atomic Number (Z) = 92
- Mass Number (A) = 234

4. **Protactinium-234**: \( _{91}^{234}Pa \)
- Atomic Number (Z) = 91
- Mass Number (A) = 234

Now, let's identify isotopes and isobars:

### Step 1: Identify Isotopes
- **Uranium-238** and **Uranium-234**: Both have the same atomic number (92), thus they are isotopes.
- **Uranium-234** and **Protactinium-234**: They have different atomic numbers (92 for U and 91 for Pa), so they are not isotopes.

### Step 2: Identify Isobars
- **Thorium-234** and **Uranium-234**: Both have the same mass number (234), thus they are isobars.
- **Thorium-234** and **Protactinium-234**: Both have the same mass number (234), thus they are isobars.
- **Uranium-238** does not match with any other nucleus in terms of mass number.

### Final Results
- **Isotopes**: \( _{92}^{238}U \) and \( _{92}^{234}U \)
- **Isobars**: \( _{90}^{234}Th \), \( _{91}^{234}Pa \), and \( _{92}^{234}U \)

### Summary
- Isotopes: \( _{92}^{238}U \) and \( _{92}^{234}U \)
- Isobars: \( _{90}^{234}Th \), \( _{91}^{234}Pa \), and \( _{92}^{234}U \)