Atomic Structure (Class 11): Quantum Numbers and Electronic Configuration Explained

The four quantum numbers

The three filling rules

1. Aufbau principle — orbitals fill from lowest energy upward, following increasing (n + l); where two are equal, the lower n fills first.
2. Pauli exclusion principle — no two electrons in an atom share all four quantum numbers, so an orbital holds at most two electrons and only with opposite spins.
3. Hund's rule — within a subshell, every orbital takes one electron before any takes a second, and those single electrons have parallel spins.

The maximum number of electrons in a shell is 2n², and in a subshell 2(2l + 1). Both follow directly from the allowed values above rather than needing separate memorisation.

Why chromium and copper are exceptions

Expected configurations would be [Ar] 3d⁴ 4s² for chromium and [Ar] 3d⁹ 4s² for copper. The observed ones are:

Exactly half-filled and completely filled subshells carry extra stability, from their symmetrical charge distribution and greater exchange energy. Because 3d and 4s are very close in energy, promoting one 4s electron costs little and buys that stability.

FAQs

What do the four quantum numbers describe?

n gives the shell, l the subshell shape, ml the orbital's orientation, and ms the electron's spin. Together they identify an electron uniquely.

Why is chromium 3d⁵ 4s¹?

A half-filled 3d subshell is unusually stable, and since 3d and 4s are close in energy, promoting one 4s electron is energetically worthwhile.

Which electrons are removed first when forming a cation?

Those in the outermost shell — 4s before 3d for first-row transition metals.

How many electrons fit in a shell?

2n², so 2 in the first shell, 8 in the second, 18 in the third.