Organic Chemistry · Structure and Bonding
Atomic Structure: Orbitals
On this page 9 sections
In 30 seconds
If the previous topic described where the atom's mass lives, this one describes where its electrons live — and electrons do not behave like tiny planets. In the 1920s, physicists showed that an electron is both a particle and a wave, and its position can never be pinned down exactly. Instead, we describe electrons with orbitals: regions of space where an electron is most likely to be found.
An orbital A region of space where an electron is most likely to be found is not a path — it is a probability map. Orbital sizes, shapes, and energies are fixed by a set of quantum numbers, and those shapes are the direct ancestors of the covalent bonds in every organic molecule. This topic focuses on the orbitals that matter most for organic chemistry: carbon's 1s, 2s, and 2p orbitals.
Why this matters
Almost everything in this book traces back to orbital shape.
- Bonding is orbital overlap. When two atoms bond, their orbitals merge; directional p orbitals (vs. spherical s orbitals) explain why bonds form at specific angles.
- Hybridization is orbital mixing. Later this chapter, carbon's 2s and 2p orbitals mix into hybrids pointing at a tetrahedron's corners — the source of methane's 109.5° bond angles.
- Spectroscopy reads orbital energies: the gaps between orbitals are exactly what ultraviolet and visible spectroscopy measure.
- Periodic trends: orbital size explains why atoms grow larger down a column of the periodic table.
The college version
Core Concepts
Electrons as waves: the de Broglie idea
In 1924, Louis de Broglie proposed that any moving particle has a wavelength. For a particle of mass m moving at speed v, the wavelength λ is:
λ= hmv
where h = 6.626 × 10-34 J·s is Planck's constant. A baseball's wavelength is undetectably tiny, but an electron's is comparable to atomic dimensions — electron waves physically fit inside atoms, and this wave behavior governs where electrons settle.
Quantum numbers: the atom's address system
Four quantum numbers fully describe an electron in an atom:
- Principal quantum number One of four numbers (n, ℓ, mℓ, ms) describing an electron's state Full entry → n (1, 2, 3, …): sets the size and energy of the orbital. Larger n = bigger orbital, higher energy, farther from the nucleus.
- Angular momentum quantum number ℓ (0 to n - 1): sets the shape. ℓ= 0 is an s orbital Spherical orbital with ℓ= 0 Full entry → (spherical), ℓ= 1 is a p orbital Dumbbell-shaped orbital with ℓ= 1, oriented along an axis Full entry → (dumbbell), ℓ= 2 is a d orbital (cloverleaf).
- Magnetic quantum number mℓ (-ℓ to +ℓ): sets the orientation in space — for ℓ= 1, three p orbitals px, py, pz point along the three axes.
- Spin quantum number ms (+12 or -12): the electron's intrinsic "spin," up or down.
A specific orbital is named by its n and ℓ: 1s, 2s, 2p, 3s, 3p, 3d, and so on.
Orbital shapes and nodes
The shapes matter because they become bonds:
- s orbitals are spheres centered on the nucleus: a 1s is small, a 2s larger (with a spherical node A region where the probability of finding an electron is zero Full entry → inside — a shell where the probability of finding the electron is zero).
- p orbitals are dumbbells: two lobes on opposite sides of the nucleus along the x, y, or z axis, with the nucleus at a node — a plane of zero probability between the lobes. Each p orbital holds two electrons.
- d orbitals have four-lobed cloverleaf shapes (five orientations), which matter for transition metals but rarely for carbon chemistry.
A useful pattern: the number of nodes in an orbital equals n - 1. The 1s has zero nodes; the 2s has one (spherical); each 2p has one (planar).
Orbital energies in hydrogen
For a hydrogen atom — one proton, one electron — the energy of an orbital depends only on n:
En = -RH 1n2
where RH = 2.18 × 10-18 J is the Rydberg constant. The negative sign means the electron is bound — energy must be added to remove it; the 1s orbital (n = 1) is the lowest-energy "ground state."
For multi-electron atoms like carbon, orbital energies also depend on ℓ (2p is higher in energy than 2s), because inner electrons shield the outer ones from the full nuclear charge. The next topic uses this energy ordering to write configurations.
How It Works / Step-by-Step Process
To name and describe any orbital:
- Read off n from the number in the orbital name (1s → n = 1).
- Read off ℓ from the letter (s → 0; p → 1; d → 2) and check it is less than n.
- Count orientations: 2ℓ+ 1 orbitals of that type (p gives 3).
- Count nodes: n - 1.
- Capacity: two electrons per orbital, opposite spins.
Common Confusions
| Common Confusion | Correct Understanding |
|---|---|
| "An orbital is a fixed orbit like a planet's path." | An orbital is a probability cloud, not a trajectory; the electron can be anywhere in it. |
| "s and p orbitals have the same shape." | s orbitals are spheres; p orbitals are dumbbells with a node at the nucleus. |
| "2p is bigger than 1s, so 2p is closer to the nucleus." | Bigger n means farther from the nucleus and higher energy, not closer. |
| "Each p orbital can hold 6 electrons." | Each orbital holds 2 electrons; the three p orbitals together hold 6. |
| "All electrons in an atom can have identical quantum numbers." | Pauli's exclusion principle forbids it — two electrons share an orbital only with opposite spins. |
| "The electron orbits the nucleus like the Moon orbits Earth." | Electrons are waves with smeared-out positions; classical orbits fail to describe them — that was the point of quantum mechanics. |
Eli explains
The same idea, in plain words
Explain it like I’m 10
An electron is like a bumblebee around a flower: you can't say where it is at any second, but you can map where it visits most. An orbital is that map — a fuzzy cloud of where the electron probably is. Some clouds are round like a balloon (s orbitals); some are two balloons tied together (p orbitals).
Worked example
Example 1: How many nodes does a 3p orbital have?
The formula before substitution:
nodes = n - 1
Substituting n = 3:
nodes = 3 - 1 = 2
A 3p orbital has two nodes: one planar node through the nucleus (like every p orbital) and one spherical node; its lobes are also larger than a 2p orbital's because n is bigger.
Example 2: Energy of an electron in the 2s orbital of hydrogen
The formula before substitution:
En = -RH 1n2
Substituting RH = 2.18 × 10-18 J and n = 2:
E2 = -(2.18 × 10-18 J) × 122 = -(2.18 × 10-18 J) × 14 = -5.45 × 10-19 J
Compared with the ground state E1 = -2.18 × 10-18 J, the 2s electron is higher in energy (less negative, less tightly bound). Excitation from 1s to 2s costs:
ΔE = E2 - E1 = (-5.45 × 10-19 J) - (-2.18 × 10-18 J) = 1.64 × 10-18 J
This is exactly the energy a photon must carry to be absorbed — the principle behind all atomic spectroscopy.
Example 3: How many orbitals are in the second shell?
For n = 2, ℓ can be 0 or 1. Orbitals of each type: 2ℓ+ 1:
s orbitals: 2(0) + 1 = 1
p orbitals: 2(1) + 1 = 3
Total in the second shell: 1 + 3 = 4 orbitals, each holding two electrons, so the shell caps at 8 — the basis of the "octet" you will meet in Lewis structures.
Key takeaways
- An orbital is a probability region, not a path; electrons are waves, not orbiting particles.
- Four quantum numbers — n, ℓ, mℓ, ms — fully specify an electron.
- ℓ= 0 → s (sphere); ℓ= 1 → p (three dumbbells along x, y, z); ℓ= 2 → d (cloverleaf).
- Each orbital holds two electrons max (opposite spins) — Pauli exclusion.
- Nodes = n - 1; every p orbital has a node at the nucleus.
- Hydrogen orbital energy depends only on n: En = -RH/n2.
- In multi-electron atoms, energy rises with n and ℓ: 1s < 2s < 2p < 3s < 3p …
- Organic chemistry is dominated by s and p orbitals; d and f orbitals rarely participate in carbon bonding.
Check yourself
6 review questions from the chapter. Try each one, then open the answer.
What physical quantity does an orbital represent?
Show answer
An orbital is a region of space where an electron is most likely to be found — a probability distribution, not a path.
List the four quantum numbers and the property each describes.
Show answer
n (size/energy), ℓ (shape), mℓ (orientation), ms (spin).
How many nodes does a 2p orbital have? A 3s orbital?
Show answer
A 2p orbital has n - 1 = 1 node; a 3s orbital has 3 - 1 = 2 nodes.
How many electrons can the three 2p orbitals of carbon hold in total?
Show answer
Six — two per orbital × three orbitals.
Calculate the energy of an electron in the n = 3 level of hydrogen using En = -RH/n2.
Show answer
E3 = -(2.18 × 10-18 J) × (1/9) = -2.42 × 10-19 J.
Why can an electron's wave nature be ignored for a baseball but not for an electron?
Show answer
The de Broglie wavelength λ= h/(mv) is inversely proportional to mass: a baseball's wavelength is unimaginably small, while an electron's is comparable to atomic size, so wave behavior dominates inside atoms.
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- orbital
- A region of space where an electron is most likely to be found
- quantum number
- One of four numbers (n, ℓ, mℓ, ms) describing an electron's state
- s orbital
- Spherical orbital with ℓ= 0
- p orbital
- Dumbbell-shaped orbital with ℓ= 1, oriented along an axis
- node
- A region where the probability of finding an electron is zero
- de Broglie wavelength
- The wavelength associated with a moving particle, λ= h/(mv)
- Rydberg constant (RH)
- 2.18 × 10-18 J; scale of hydrogen orbital energies
- Pauli exclusion principle
- No two electrons in an atom can have all four quantum numbers identical
- π orbital
- MO from side-by-side p-orbital overlap; density above and below the axis
Sources & references
This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.
Educational content only. It is not medical, legal or professional advice. Found an error? Tell us.