Atomic Orbitals and Quantum Numbers
High-Yield Summary
- Four quantum numbers fully describe any electron in an atom: n (principal), l (angular momentum), mₗ (magnetic), mₛ (spin).
- n (any positive integer) gives the shell/energy level; a larger n means a larger, higher-energy shell farther from the nucleus, and sets the shell's max electron capacity.
- l (0 to n − 1) sets the subshell shape: l = 0 → s (spherical), l = 1 → p (dumbbell), l = 2 → d (cloverleaf), l = 3 → f (complex).
- mₗ (−l to +l) sets orbital orientation and how many orbitals exist in a subshell — e.g. p (l=1) has 3 orbitals (mₗ = −1, 0, +1): pₓ, p_y, p_z.
- mₛ (+1/2 or −1/2) is electron spin — the reason each orbital holds a maximum of 2 electrons.
Shell Capacity by n
| n (shell) | Subshells present / max electrons |
|---|---|
| n = 1 | 1s → 2 electrons |
| n = 2 | 2s + 2p → 8 electrons |
| n = 3 | 3s + 3p + 3d → 18 electrons |
| n = 4 | 4s + 4p + 4d + 4f → 32 electrons |
Key Terms
- Orbital
- Region of space (from solving Schrödinger's equation) with high probability of finding an electron — replaces Bohr's fixed-orbit picture.
- Principal quantum number (n)
- Positive integer identifying the shell/energy level; sets the shell's maximum electron capacity (2n²).
- Angular momentum quantum number (l)
- Ranges 0 to n − 1; determines subshell shape (s, p, d, f).
- Magnetic quantum number (mₗ)
- Ranges −l to +l; specifies orbital orientation and number of orbitals per subshell.
- Spin quantum number (mₛ)
- +1/2 or −1/2; each orbital holds at most 2 electrons, one of each spin.
Common MCAT Trap
- l ranges from 0 to n − 1, not 1 to n — n = 1 only allows l = 0 (1s), no 1p exists.
- mₗ range depends on l, not n — a p subshell always has exactly 3 orbitals (mₗ = −1, 0, +1) regardless of which shell it's in.
- Shell capacity follows 2n² — don't just memorize 2/8/18/32 without knowing it derives from summing each subshell's orbital count × 2.
Quick Recall
What are the four quantum numbers and what does each describe?
How many orbitals are in a d subshell, and how many electrons can it hold?
Why does each orbital hold a maximum of 2 electrons?
What is the maximum electron capacity of the n = 3 shell, and which subshells make it up?