Which of the following nuclides has the magic number of both protons and neutrons?

Options

A. `Sn_50^115`
B. `Pb_82^206`
C. `Pb_82^208`
D. `Sn_50^118`

Answer

To determine which nuclide has both a magic number of protons and neutrons, we will follow these steps:

### Step 1: Understand Magic Numbers
Magic numbers are specific numbers of protons or neutrons that result in a more stable nucleus. The known magic numbers for protons are:
- 2, 8, 20, 28, 50, 82

And for neutrons:
- 2, 8, 20, 28, 50, 82, 126

### Step 2: Analyze Each Given Nuclide
We will analyze the given nuclides one by one to check if both the number of protons and neutrons correspond to magic numbers.

1. **Nuclide: Sn-115**
- Atomic Number (Protons) = 50 (which is a magic number)
- Mass Number = 115
- Neutrons = Mass Number - Protons = 115 - 50 = 65 (not a magic number)

2. **Nuclide: Pb-206**
- Atomic Number (Protons) = 82 (which is a magic number)
- Mass Number = 206
- Neutrons = Mass Number - Protons = 206 - 82 = 124 (not a magic number)

3. **Nuclide: Pb-208**
- Atomic Number (Protons) = 82 (which is a magic number)
- Mass Number = 208
- Neutrons = Mass Number - Protons = 208 - 82 = 126 (which is a magic number)

4. **Nuclide: Sn-118**
- Atomic Number (Protons) = 50 (which is a magic number)
- Mass Number = 118
- Neutrons = Mass Number - Protons = 118 - 50 = 68 (not a magic number)

### Step 3: Conclusion
From the analysis, only **Pb-208** has both a magic number of protons (82) and neutrons (126). Therefore, the correct answer is:

**Option 3: Pb-208**

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