Which of the following sets of quantum numbers represents the highest energy of an atom?

Options

A. `n = 3, l = 1, m = 1, s = +1//2`
B. `n = 3, l = 2, m = 1, s = +1//2`
C. `n = 4, l = 0, m = 0, s = +1//2`
D. `n = 3, l = 0, m = 0, s = +1//2`

Explanation

To determine which set of quantum numbers represents the highest energy of an atom, we will use the n + l rule. The energy of an electron in an atom is influenced by the principal quantum number (n) and the azimuthal quantum number (l). According to the n + l rule, the higher the sum of n + l, the higher the energy of the electron.

### Step-by-Step Solution:

1. **Identify the Quantum Numbers**: We need to analyze the provided options, which consist of sets of quantum numbers (n, l).

2. **Calculate n + l for Each Option**:
- **Option A**:
- n = 3, l = 1
- n + l = 3 + 1 = 4
- **Option B**:
- n = 3, l = 2
- n + l = 3 + 2 = 5
- **Option C**:
- n = 4, l = 0
- n + l = 4 + 0 = 4
- **Option D**:
- n = 3, l = 0
- n + l = 3 + 0 = 3

3. **Compare n + l Values**:
- Option A: n + l = 4
- Option B: n + l = 5
- Option C: n + l = 4
- Option D: n + l = 3

4. **Determine the Highest n + l Value**:
- The maximum value of n + l is 5, which occurs in **Option B**.

5. **Conclusion**:
- Therefore, the set of quantum numbers that represents the highest energy of an atom is **Option B**.