Quantum Numbers for Electrons in an Oxygen Atom (Z = 8)
Question:
For an oxygen atom (Z = 8), list the quantum numbers n, l, ml, and ms for each electron. Also compute the z-component of orbital angular momentum:
Lz = ml ℏ
Use: ℏ = 1.05 × 10−34 J·s
Answer:
Step 1: Electron Configuration of Oxygen (Z = 8)
Total electrons = 8
Electron configuration: 1s² 2s² 2p⁴
Step 2: Understanding Quantum Numbers
- n: Principal quantum number (energy level)
- l: Orbital angular momentum quantum number
- l = 0 (s orbital), l = 1 (p orbital)
- ml: Magnetic quantum number → ranges from −l to +l
- ms: Spin quantum number → ±½
Step 3: Assigning Quantum Numbers for Each Electron
Following the Aufbau principle, Pauli exclusion, and Hund’s rule:
| Electron | n | l | ml | ms | Lz = ml ℏ (J·s) |
|---|---|---|---|---|---|
| 1 | 1 | 0 | 0 | +½ | 0 |
| 2 | 1 | 0 | 0 | −½ | 0 |
| 3 | 2 | 0 | 0 | +½ | 0 |
| 4 | 2 | 0 | 0 | −½ | 0 |
| 5 | 2 | 1 | −1 | +½ | −1.05×10⁻³⁴ |
| 6 | 2 | 1 | 0 | +½ | 0 |
| 7 | 2 | 1 | +1 | +½ | +1.05×10⁻³⁴ |
| 8 | 2 | 1 | −1 | −½ | −1.05×10⁻³⁴ |
✅ Conclusion:
All 8 electrons of oxygen are correctly assigned quantum numbers following the Pauli exclusion principle and Hund’s rule. The z-component of orbital angular momentum, Lz, is calculated for each electron using: Lz = ml ℏ
All 8 electrons of oxygen are correctly assigned quantum numbers following the Pauli exclusion principle and Hund’s rule. The z-component of orbital angular momentum, Lz, is calculated for each electron using: Lz = ml ℏ