Grade 10

Orbitals, electron configuration, quantum numbers

Where electrons are likely to be found around a nucleus, and how that pattern fills up the periodic table.

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IntuitionIntuition: a cloud, not an orbit

An electron in an atom is not a tiny planet on a fixed track. Quantum mechanics describes it with a wave function $\psi$ ; its square $|\psi|^2$ tells how likely the electron is to be found at each point. An orbital is the region of high probability, drawn as a cloud.

Each dot is a possible position of the electron. Change

n

l

m

s

orbitals are spheres,

p

orbitals have two lobes,

d

orbitals mostly four. Orange and blue show the sign of

\psi

, not an electric charge.

SchoolSchool level: the quantum numbers

Definition: Quantum numbers

$n = 1, 2, 3, \dots$ sets the shell and the energy scale. $l = 0, 1, \dots, n-1$ sets the subshell and its shape ( $s, p, d, f$ ). $m$ runs from $-l$ to $+l$ and sets the orientation. The spin $m_s = \pm\tfrac12$ distinguishes the two electrons that can share one orbital.

\text{orbitals in shell } n = n^2,\qquad \text{electrons} \le 2n^2

Electrons fill orbitals from low to high energy (Aufbau), at most two per orbital with opposite spins (Pauli), and spread over orbitals of equal energy with parallel spins before pairing up (Hund).

Choose an atomic number

Z

: the overlay lists the electron configuration. Orange electrons are the valence electrons.

Example: Iron, $Z = 26$

Write the electron configuration of iron.

Solution

$\ce{Fe}$ : $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^6\,4s^2$ . The $4s$ subshell fills before $3d$ , but iron loses its $4s$ electrons first when it forms $\ce{Fe^2+}$ and $\ce{Fe^3+}$ .