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Orbital box diagrams (also called orbital diagrams or “arrows in boxes”) show exactly how electrons are placed in each orbital, including their spins. They’re the clearest way to see Hund’s rule and the Pauli exclusion principle in action, and they let you count unpaired electrons at a glance.
In this article, diagrams are written in text. Each orbital is a pair of square brackets, and electrons are ↑ (spin up) or ↓ (spin down):
[↑↓]a filled orbital[↑ ]a half-filled orbital[ ]an empty orbital
A p subshell has three boxes, a d subshell five, and an f subshell seven. If you need the full method first, see how to draw orbital diagrams.
The three rules
- Aufbau: fill lower-energy subshells first (1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p…).
- Pauli: at most two electrons per box, with opposite spins.
- Hund: within a subshell, put one electron in each box (same spin) before pairing any.
Section A: drawing diagrams
Q1. Draw the orbital box diagram for nitrogen (Z = 7).
Q2. Draw the orbital box diagram for oxygen (Z = 8). How many unpaired electrons does it have?
Q3. Draw the diagram for the valence subshells (3s and 3p) of phosphorus (Z = 15).
Q4. Draw the 4s and 3d boxes for iron (Z = 26). How many unpaired electrons does an iron atom have?
Section B: spotting errors
Each diagram below breaks a rule. Name the rule and correct the diagram.
Q5. Carbon, 2p subshell: [↑↓] [ ] [ ]
Q6. Helium, 1s: [↑↑]
Q7. Beryllium: 1s [↑↓], 2s [↑ ], 2p [↑ ] [ ] [ ]
Q8. Nitrogen, 2p subshell: [↑ ] [↓ ] [↑ ]
Section C: ions and magnetism
Q9. Draw the 3d boxes for Fe²⁺ and Fe³⁺. Which has more unpaired electrons?
Q10. Which of these atoms or ions are paramagnetic (have unpaired electrons)? Zn, Zn²⁺, Cu²⁺, O, Ne.
Section D: exceptions and challenge
Q11. Chromium (Z = 24) has the configuration [Ar] 3d⁵ 4s¹ rather than [Ar] 3d⁴ 4s². Draw both diagrams and count unpaired electrons in each. Suggest why the actual configuration is favoured.
Q12. A neutral atom in its ground state has the diagram below for its outer subshells. Identify the element.
3s [↑↓] 3p [↑↓] [↑↓] [↑ ]
Answer key
A1. Nitrogen: 1s² 2s² 2p³
1s [↑↓] 2s [↑↓] 2p [↑ ] [↑ ] [↑ ]
The three 2p electrons go into separate boxes with parallel spins (Hund’s rule). Nitrogen has 3 unpaired electrons.
A2. Oxygen: 1s² 2s² 2p⁴
1s [↑↓] 2s [↑↓] 2p [↑↓] [↑ ] [↑ ]
After one electron in each 2p box, the fourth pairs up in the first box. Oxygen has 2 unpaired electrons, which is why O₂ is paramagnetic (see paramagnetic vs diamagnetic).
A3. Phosphorus: [Ne] 3s² 3p³
3s [↑↓] 3p [↑ ] [↑ ] [↑ ]
Three unpaired 3p electrons, the same pattern as nitrogen above it in group 15.
A4. Iron: [Ar] 3d⁶ 4s²
4s [↑↓] 3d [↑↓] [↑ ] [↑ ] [↑ ] [↑ ]
Five electrons go singly into the five 3d boxes, and the sixth pairs in the first box. Iron has 4 unpaired electrons.
A5.
Breaks Hund’s rule: the two 2p electrons are paired in one box while other boxes are empty. Correct: [↑ ] [↑ ] [ ].
A6.
Breaks the Pauli exclusion principle: two electrons in one orbital must have opposite spins. Correct: [↑↓].
A7.
Breaks the Aufbau principle: the 2s orbital isn’t full, yet an electron has been placed in the higher-energy 2p. Beryllium (4 electrons) is 1s [↑↓] 2s [↑↓], with the 2p boxes empty.
A8.
Breaks Hund’s rule: in the ground state, singly occupied boxes in a subshell have parallel spins. Correct: [↑ ] [↑ ] [↑ ]. (A diagram with one spin reversed describes an excited state.)
A9.
Transition metals lose their 4s electrons first when forming ions (see electron configuration of ions).
- Fe²⁺: [Ar] 3d⁶ → 3d
[↑↓] [↑ ] [↑ ] [↑ ] [↑ ]→ 4 unpaired. - Fe³⁺: [Ar] 3d⁵ → 3d
[↑ ] [↑ ] [↑ ] [↑ ] [↑ ]→ 5 unpaired.
Fe³⁺ has more unpaired electrons, and its half-filled 3d subshell is particularly stable.
A10.
- Zn: [Ar] 3d¹⁰ 4s², all paired → diamagnetic.
- Zn²⁺: [Ar] 3d¹⁰, all paired → diamagnetic.
- Cu²⁺: [Ar] 3d⁹ → one unpaired electron → paramagnetic.
- O: 2 unpaired (see A2) → paramagnetic.
- Ne: all paired → diamagnetic.
Paramagnetic: Cu²⁺ and O. To count unpaired electrons quickly, see how to count unpaired electrons.
A11.
Predicted [Ar] 3d⁴ 4s²:
4s [↑↓] 3d [↑ ] [↑ ] [↑ ] [↑ ] [ ] → 4 unpaired.
Actual [Ar] 3d⁵ 4s¹:
4s [↑ ] 3d [↑ ] [↑ ] [↑ ] [↑ ] [↑ ] → 6 unpaired.
Because 4s and 3d are very close in energy, moving one electron from 4s to 3d costs little. In return, the atom gets a half-filled 3d subshell, avoids the repulsion of a paired 4s orbital, and gains extra exchange energy from having more electrons with parallel spins. The net effect favours 3d⁵ 4s¹. Copper (3d¹⁰ 4s¹) is the other well-known case. See electron configuration exceptions.
A12.
Count the electrons: [Ne] core (10) + 3s² (2) + 3p⁵ (5) = 17. The element is chlorine. It has one unpaired electron, consistent with forming one bond.
A reliable routine for any orbital diagram
When you meet a new atom or ion in an exam, a fixed routine prevents most errors.
First, find the total number of electrons. For a neutral atom this is the atomic number. For a positive ion subtract the charge, and for a negative ion add it. Write this number down before you draw anything, because the final check depends on it.
Second, write the full or noble-gas configuration using the filling order. Doing this in words first (for example, [Ar] 3d⁶ 4s² for iron) means you only have to think about the order once. If the species is a transition-metal ion, remove electrons from 4s before 3d at this stage, not while drawing.
Third, draw only the subshells you need. Examiners usually want the valence subshells, and drawing every core box wastes time and adds chances to miscount. A noble-gas symbol in square brackets can stand in for the core.
Fourth, fill each subshell in two passes. In the first pass, place one up-arrow in every box. In the second pass, go back to the first box and add down-arrows until you run out of electrons. This two-pass habit makes Hund’s rule automatic.
Finally, count the arrows and compare with the number from the first step, then count the boxes with a single arrow to find the number of unpaired electrons. If a question asks about magnetism, that last number is your answer: any unpaired electrons make the species paramagnetic.
With practice, this routine takes well under a minute and works for every element in the first four periods. Heavier elements follow the same rules, although more of them show exceptions like chromium and copper.
Common mistakes in orbital diagrams
- Pairing too early. Always fill every box in a subshell singly first.
- Opposite spins in half-filled boxes. Unpaired electrons in the same subshell should all point the same way in the ground state.
- Forgetting that 4s fills before 3d but empties first. For transition-metal ions, remove 4s electrons before 3d.
- Drawing the wrong number of boxes. s = 1, p = 3, d = 5, f = 7.
- Losing count. Check that the total number of arrows equals the number of electrons in the atom or ion.
Key takeaways
- Orbital box diagrams show each orbital and each electron’s spin.
- Use Aufbau for order, Pauli for at most two opposite spins per box, and Hund for spreading out before pairing.
- Unpaired electrons are easy to count from a diagram and predict paramagnetism.
- Transition-metal ions lose 4s electrons first; chromium and copper are the classic exceptions to the filling order.
- Generate the diagram for any element with the electron configuration generator.
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