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

Options

A. `n=4, l=3, m=+4, 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 need to calculate the value of \( n + l \) for each option, where \( n \) is the principal quantum number and \( l \) is the azimuthal quantum number. The higher the \( n + l \) value, the higher the energy level of the electron.

### Step-by-Step Solution:

1. **Identify the Quantum Numbers for Each Option:**
- **Option 1:** \( n = 4, l = 3 \)
- **Option 2:** \( n = 3, l = 2 \)
- **Option 3:** \( n = 4, l = 0 \)
- **Option 4:** \( n = 3, l = 0 \)

2. **Calculate \( n + l \) for Each Option:**
- **Option 1:**
\[ n + l = 4 + 3 = 7 \]
- **Option 2:**
\[ n + l = 3 + 2 = 5 \]
- **Option 3:**
\[ n + l = 4 + 0 = 4 \]
- **Option 4:**
\[ n + l = 3 + 0 = 3 \]

3. **Compare the \( n + l \) Values:**
- Option 1: \( n + l = 7 \)
- Option 2: \( n + l = 5 \)
- Option 3: \( n + l = 4 \)
- Option 4: \( n + l = 3 \)

4. **Determine the Highest Energy:**
- The highest \( n + l \) value is **7** from **Option 1**.

### Conclusion:
The set of quantum numbers that represents the highest energy of an atom is **Option 1: \( n = 4, l = 3, m = +4, s = +\frac{1}{2} \)**.

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