Which of the following nuclei are doubly magic?

Options

A. `._(92)U^(238)`
B. `._(2)He^(4)`
C. `._(8)O^(16)`
D. `._(82)Pb^(208)`

Explanation

To determine which of the following nuclei are doubly magic, we need to understand the concept of magic numbers in nuclear chemistry. A nucleus is considered doubly magic if both the number of protons and the number of neutrons are magic numbers. The recognized magic numbers are 2, 8, 20, 28, 50, 82, and 126.

### Step-by-Step Solution:

1. **Identify the Nuclei and Their Composition**:
- We need to analyze the given nuclei and their respective numbers of protons and neutrons.
- For example, let's consider the following nuclei:
- Uranium-238 (U-238): Protons = 92, Neutrons = 146
- Helium-4 (He-4): Protons = 2, Neutrons = 2
- Oxygen-16 (O-16): Protons = 8, Neutrons = 8
- Lead-208 (Pb-208): Protons = 82, Neutrons = 126

2. **Check Each Nucleus Against Magic Numbers**:
- For each nucleus, we will check if both the number of protons and neutrons are magic numbers.
- **Uranium-238**:
- Protons = 92 (not a magic number)
- Neutrons = 146 (not a magic number)
- **Helium-4**:
- Protons = 2 (magic number)
- Neutrons = 2 (magic number)
- **Oxygen-16**:
- Protons = 8 (magic number)
- Neutrons = 8 (magic number)
- **Lead-208**:
- Protons = 82 (magic number)
- Neutrons = 126 (magic number)

3. **Determine Which Nuclei are Doubly Magic**:
- From the checks:
- Helium-4: Both protons and neutrons are magic → Doubly magic
- Oxygen-16: Both protons and neutrons are magic → Doubly magic
- Lead-208: Both protons and neutrons are magic → Doubly magic
- Uranium-238: Not doubly magic
- Therefore, the doubly magic nuclei are Helium-4, Oxygen-16, and Lead-208.

### Conclusion:
The doubly magic nuclei among the given options are **Helium-4, Oxygen-16, and Lead-208**.