Orbital Shapes
The shape of an orbital is not random - it is determined by the azimuthal quantum number (l). Each type of orbital has a characteristic shape that tells you where an electron is most likely to be found. You do not need to draw these shapes from memory on the MCAT, but you must recognize them and understand what they mean.
s Orbitals (l = 0)
s orbitals are spherical. The electron density is evenly distributed in all directions from the nucleus. There is one s orbital per shell.
As n increases, s orbitals get larger (the electron is farther from the nucleus on average), and they develop radial nodes - spherical shells where the probability of finding the electron is zero. The 1s orbital has no nodes, the 2s has one radial node, and the 3s has two.
p Orbitals (l = 1)
p orbitals are dumbbell-shaped (or peanut-shaped), with two lobes on opposite sides of the nucleus and a nodal plane through the center where the probability of finding the electron is zero.
Orbital shapes and the four quantum numbers
Scroll sideways to see the whole map.
Where the capacities come fromA subshell has 2ℓ + 1 orbitals because mℓ runs from −ℓ to +ℓ, and each orbital holds two electrons because ms has two values. So s holds 2, p holds 6, d holds 10, f holds 14. Nothing there needs memorising separately.
What a node isA node is a surface where the probability of finding the electron is zero. The pinch at the centre of every p orbital is one; the two planes that separate a d cloverleaf's four lobes are two more. Higher ℓ means more nodal planes, which is most of why higher-ℓ subshells sit higher in energy.
Lobes are not pathsThe surfaces drawn here are probability contours, usually the boundary enclosing about 90 % of the electron density, not orbits. The plus and minus signs are the phase of the wavefunction, and they are what decides whether two orbitals overlap constructively into a bond.
There are three p orbitals per shell (starting at n = 2), oriented along the x, y, and z axes: px, py, and pz. They are identical in shape and energy but point in different directions.
d Orbitals (l = 2)
d orbitals have more complex shapes, generally described as cloverleaf patterns with four lobes. There are five d orbitals per shell (starting at n = 3).
Four of the five d orbitals have four lobes arranged in a cloverleaf pattern but oriented differently in space. The fifth (dz²) looks different - it has two lobes along the z-axis with a donut (torus) in the xy-plane.
The MCAT will not ask you to draw d orbital shapes, but you should know they exist starting at n = 3, there are five of them, and they hold up to 10 electrons total.
f Orbitals (l = 3)
f orbitals have even more complex shapes with multiple lobes. There are seven f orbitals per shell (starting at n = 4), holding up to 14 electrons.
The shapes of f orbitals are not tested on the MCAT. What matters is knowing that f subshells exist, they appear in the lanthanide and actinide series, and they hold up to 14 electrons.
Nodes
A node is a region where the probability of finding the electron is exactly zero. There are two types:
- Radial (spherical) nodes: Spherical shells within the orbital where electron density is zero. Number = n - l - 1.
- Angular (planar) nodes: Flat planes or cones through the nucleus. Number = l.
- Total nodes = n - 1
| Orbital | n | l | Radial nodes (n-l-1) | Angular nodes (l) | Total nodes (n-1) |
|---------|---|---|---------------------|-------------------|-------------------|
| 1s | 1 | 0 | 0 | 0 | 0 |
| 2s | 2 | 0 | 1 | 0 | 1 |
| 2p | 2 | 1 | 0 | 1 | 1 |
| 3s | 3 | 0 | 2 | 0 | 2 |
| 3p | 3 | 1 | 1 | 1 | 2 |
| 3d | 3 | 2 | 0 | 2 | 2 |
Summary
| Subshell | l | Shape | Orbitals | Max electrons | First appears at n = |
|----------|---|-------|----------|--------------|---------------------|
| s | 0 | Sphere | 1 | 2 | 1 |
| p | 1 | Dumbbell | 3 | 6 | 2 |
| d | 2 | Cloverleaf | 5 | 10 | 3 |
| f | 3 | Complex | 7 | 14 | 4 |
1 radial node, 1 angular node. Total nodes = n - 1 = 3 - 1 = 2. Angular nodes = l = 1. Radial nodes = total - angular = 2 - 1 = 1.
Cloverleaf shape (four lobes), first appearing at n = 3. Since l can range from 0 to n-1, the d subshell (l = 2) requires at least n = 3. There are five d orbitals, holding up to 10 electrons.