Orbitals and electrons in boxes
Introduced| English | Meaning |
|---|---|
| orbital/ˈɔːbɪtl/ | A quantum state associated with an electron's spatial distribution around a nucleus, often represented by a region of high probability. |
| spin/spɪn/ | A property of an electron; two electrons in one orbital must have opposite spins. |
| unpaired electron/ʌnˈpeəd ɪˈlektrɒn/ | An electron occupying an orbital without a second electron of opposite spin. |
| free radical/friː ˈrædɪkl/ | A species containing one or more unpaired electrons. |
| repulsion/rɪˈpʌlʃn/ | An interaction that tends to push particles or objects apart. |
Four electrons do not always make two pairs
- Draw an orbital 轨道 as a box and an electron as an arrow. The arrows label spin 自旋 states, not the paths electrons travel around the nucleus.
- This notation distinguishes pairs from unpaired electrons 未成对电子. A free radical 自由基 has at least one unpaired electron, rather than merely having a negative charge or a lone pair.
Apply both filling rules
- At most two electrons share one orbital, with opposite spins. In a set of equal-energy orbitals within a sub-shell, put one electron in each with parallel spins before adding a second to any box.
- This lower-energy arrangement limits repulsion 排斥 between electrons sharing an orbital. Nitrogen's 2p³ occupation has one electron in each of three 2p orbitals; pairing two while leaving one orbital empty is not its ground state.
Count occupied boxes, pairs and total arrows separately.
Filling the orbitals
Drag the proton number up and watch electrons fill the shells and sub-shells in order — 1s, 2s, 2p … — each box holding a spin-paired pair.
Each orbital can hold up to two electrons, which must have the same spin.
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False. Two electrons in one orbital must have opposite spins, which is why ‘electrons in boxes’ show two arrows pointing opposite ways.
Two electrons sharing one orbital must:
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Electrons in the same orbital have opposite spins; this is why a box holds at most two arrows pointing opposite ways.
Within a sub-shell, electrons:
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Filling singly first keeps the electrons apart, reducing repulsion (e.g. nitrogen's three 2p orbitals each get one).
Count pairs in the shell that was asked for
- Oxygen is $1\mathrm{s}^2\,2\mathrm{s}^2\,2\mathrm{p}^4$. Its 2p electrons form one pair and two unpaired electrons; adding the 2s pair gives two pairs in the $n=2$ shell.
- A question about the whole shell includes every occupied sub-shell with that $n$. A question about 2p alone excludes 2s and 1s; do not just divide the number of electrons by two.
Only the second shell is shown. The filled 1s orbital does not count towards a second-shell answer.
Co²⁺ has configuration [Ar] 3d⁷. Draw its five 3d boxes on paper. Count the pairs and unpaired electrons in 3d, then give the total number of pairs in its n = 3 shell.
Place one electron in each of the five 3d boxes, then pair two: 3d contains two pairs and three unpaired electrons. The n = 3 shell also includes one 3s pair and three 3p pairs, so it contains 1 + 3 + 2 = 6 pairs. The 1s and 2s/2p pairs are not part of n = 3.
Sketch an orbital, rather than an orbit
- An s orbital is spherical around the nucleus. A p orbital has two lobes with the nucleus between them; both lobes belong to one orbital and do not hold two electrons each.
- The three p orbitals have different orientations, conventionally $p_x$, $p_y$ and $p_z$. A drawn boundary represents the region where an electron is likely to be found, rather than a fixed circular track.
For an exam sketch, make the shape and nucleus position clear; a p orbital is not two separate s orbitals.
The shape of a p orbital is:
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An s orbital is a sphere; each p orbital is a dumbbell, and the three point along x, y and z.
Match each term to what it means.
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s is spherical, p is a dumbbell; every orbital holds 2 paired electrons, and they spread out singly first (Hund's rule).
An s orbital is spherical; a p orbital is shaped like a ______.
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The three p orbitals are dumbbells pointing along the x, y and z axes.
Sketch an s orbital and one p orbital on paper, marking the nucleus. Explain why two lobes of a p orbital do not mean two separate orbitals or a capacity of four electrons.
The s orbital is spherical around the nucleus; the p orbital has two lobes with the nucleus between them. The two lobes form one orbital, holding at most two electrons with opposite spins. They describe an electron-probability region, not two paths with two electrons each. Keep the sketches for teacher review.
Distinguish an unpaired electron from a charge
- An isolated chlorine atom has 3p⁵, so one electron is unpaired: it is a radical. Cl⁻ has 3p⁶, with all three orbitals paired; the negative charge does not make it a radical.
- Radicals are often reactive because of unpaired electrons. Use the electron arrangement to apply the definition; “charged particle” and “species with a lone pair” are not equivalent definitions.
One occupied box may contain either one electron or a pair. In d⁵ there are five singly occupied orbitals; in d⁶ there is one pair and four unpaired electrons. Check the arrows before counting pairs.
A free radical is a species that:
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An unpaired electron defines a radical. Many radicals are reactive, but reactivity alone is not the definition.
An isolated Cl atom has 3p⁵; Cl⁻ has 3p⁶. Use boxes or a clear description to decide which is a radical. Explain why a lone pair or negative charge is not enough to classify a radical.
The 3p⁵ atom has two pairs and one unpaired electron, so it is a radical. The 3p⁶ ion has three pairs and no unpaired electrons, so it is not a radical by this definition. A lone pair contains two paired electrons; a negative charge describes net charge rather than whether an electron is unpaired.
You've got it
- Opposite spins within a pair; singly occupied equal-energy orbitals before pairing.
- Count every relevant sub-shell for a shell question, but only the named sub-shell for a sub-shell question.
- An s orbital is spherical; a p orbital has two lobes within one orbital.
- A radical has an unpaired electron; a charge or a lone pair alone does not establish this.