Problem
Construct an orbital diagram for each of the following element (interpreted here as the common set \(\mathrm{N}\), \(\mathrm{O}\), \(\mathrm{Na}\), and \(\mathrm{Cl}\)) in the ground state. Use the box-and-arrow method and show the electron configuration used to justify each diagram.
Rules used to fill orbital diagrams
- Aufbau principle: fill lower-energy orbitals first (order such as \(1s, 2s, 2p, 3s, 3p,\dots\)).
- Pauli exclusion principle: an orbital holds at most 2 electrons with opposite spins (\(\uparrow\downarrow\)).
- Hund’s rule: in degenerate orbitals (like the three \(p\) orbitals), place one electron in each with parallel spin before pairing.
Visualization: Aufbau (filling order) map for common orbitals
Step 1: Determine electron counts and electron configurations
For neutral atoms, the number of electrons equals the atomic number \(Z\). Then write the ground-state electron configuration using Aufbau order.
| Element | \(Z\) | Electrons | Electron configuration (ground state) | Valence subshell(s) |
|---|---|---|---|---|
| N | 7 | 7 | \(\mathrm{1s^2\,2s^2\,2p^3}\) | \(\mathrm{2s,\,2p}\) |
| O | 8 | 8 | \(\mathrm{1s^2\,2s^2\,2p^4}\) | \(\mathrm{2s,\,2p}\) |
| Na | 11 | 11 | \(\mathrm{1s^2\,2s^2\,2p^6\,3s^1}\) | \(\mathrm{3s}\) |
| Cl | 17 | 17 | \(\mathrm{1s^2\,2s^2\,2p^6\,3s^2\,3p^5}\) | \(\mathrm{3s,\,3p}\) |
Step 2: Convert each electron configuration into an orbital diagram
Each box represents one orbital. An \(s\) subshell has 1 orbital (1 box), a \(p\) subshell has 3 orbitals (3 boxes). Arrows represent electron spins.
Box key
Empty orbital: One electron: ↑ Paired electrons: ↑↓
Nitrogen (N): \(\mathrm{1s^2\,2s^2\,2p^3}\)
Hund’s rule places the three \(2p\) electrons singly in separate \(p\) orbitals before any pairing.
Oxygen (O): \(\mathrm{1s^2\,2s^2\,2p^4}\)
After placing three parallel-spin electrons in the three \(2p\) orbitals, the fourth \(2p\) electron pairs in one orbital (Pauli exclusion requires opposite spins).
Sodium (Na): \(\mathrm{1s^2\,2s^2\,2p^6\,3s^1}\)
The \(3s\) subshell contains one valence electron, consistent with sodium’s high reactivity and typical \(+1\) ion formation.
Chlorine (Cl): \(\mathrm{1s^2\,2s^2\,2p^6\,3s^2\,3p^5}\)
The \(3p^5\) pattern produces one unpaired electron in the \(3p\) subshell, consistent with chlorine’s tendency to gain one electron to form \(\mathrm{Cl^-}\).
Common checkpoints for correctness
- Total arrows across all boxes equals \(Z\) for a neutral atom.
- No box contains more than two arrows, and paired arrows are opposite-spin (\(\uparrow\downarrow\)).
- For a \(p\) subshell, single occupancy across the three boxes occurs before any pairing (Hund’s rule).