Foundations — General electronic configuration (n−1)d¹⁻¹⁰ ns⁰⁻²

This page assumes nothing. If you have never seen a superscript on an orbital, start here and build every piece one at a time. Each symbol is earned before the parent note uses it.

0. What are we even looking at?

The parent note's headline symbol is:

$(n-1)d^{1\text{–}10}n{s}^{0\text{–}2}$

That single line hides seven ideas: the letter $n$, subtraction $n-1$, the letters $s$ and $d$, superscripts, the ranges $1$–$10$ and $0$–$2$, and the invisible ordering rule behind them. We unpack them in an order where each rests on the one before.

Look at the picture above: the address is read like a street sign. We will build it left to right, then bottom to top.

1. The atom: a nucleus and shells (the picture behind everything)

• Plain words: the nucleus pulls electrons inward; electrons stack in layers around it.
• The picture: concentric rings around a dot. Inner rings sit close to the nucleus; outer rings sit far.
• Why the topic needs it: transition-metal chemistry is entirely about which layer an electron is in — an inner layer or the outer surface. No layers, no story.

2. The symbol $n$ — the shell number

• Plain words: $n$ answers "which onion layer?"
• The picture: in the figure above, the label on each ring is its $n$.
• Why the topic needs it: the whole recipe is written "for an element in period $n$." The period number of the periodic table is the outermost shell's $n$. Period 4 → $n=4$.

3. Subshells and the symbol $\ell$ — the shape of the room

Inside each shell there are sub-rooms of different shapes. We label the shape with a second number, $\ell$.

• Plain words: $\ell$ says "what shape is this room?"
• The picture: $s$ is a round ball, $p$ is a dumbbell (two lobes), $d$ is a four-lobed clover, $f$ is more tangled still.
• Why the topic needs it: the letters $s$ and $d$ in the recipe are $\ell$-labels. "$d$" literally means "$\ell =2$". This is why the parent note says "$d$-orbitals need $\ell =2$."

This is exactly why the parent's symbol is $(n-1)d$ and not $nd$ — hold that thought for section 6. See f-Block (n-2)f orbitals filling for the same logic pushed one letter further ($f$ needs $\ell =3$, so $n\ge 4$).

4. How many electrons fit — the superscript ranges

Each subshell holds a fixed maximum number of electrons. That maximum is where the superscripts ${}^{1\text{–}10}$ and ${}^{0\text{–}2}$ come from.

• Plain words: count the rooms of that shape, then double (two electrons per room).
• The picture: five $d$-clovers side by side, each with two seats → ten seats total.
• Why the topic needs it: "$d^{1-10}$" means the $d$-subshell can hold anywhere from 1 up to its max of 10 electrons; "$s^{0-2}$" means the outer $s$ holds 0, 1, or 2 (2 being its max). The ranges are just "empty up to full."

5. Two electrons per room — and why pairs (spin)

Why does each orbital hold exactly two?

• Plain words: a room seats two, but only a ↑ and a ↓ together.
• The picture: a box with one up-arrow and one down-arrow.
• Why the topic needs it: the parent note's talk of "unpairing the $s$", "parallel spins", and exchange energy all rests on spin. Whether electrons sit paired or spread out with parallel spins decides magnetism and the Cr/Cu exceptions — see Exchange Energy and Hund's Rule and Magnetic Properties (spin-only formula).

6. The subtraction $(n-1)$ — reading the address

Now we can read the trickiest part of the symbol.

• Plain words: "$d$ is down one floor from the surface $s$."
• The picture: two labelled floors — surface $ns$ on top, inner $(n-1)d$ just below.
• Why the topic needs it: this is the literal meaning of the parent's headline. See the parent topic.

7. The hidden ordering rule — who moves in first?

The recipe never states the order electrons enter, but you cannot build a single configuration without it. That order is the Aufbau / Madelung rule, and its physical cause is penetration and shielding.

• The picture: an $s$ electron's cloud has a bump right next to the nucleus; a $d$ electron's cloud stays farther out. The $s$ therefore "wins" a lower energy slot.
• Why the topic needs it: this is precisely why $4s$ fills before $3d$ even though $4$ looks bigger than $3$ — the $(n+\ell )$ rule packages this. Full treatment in Aufbau Principle and Madelung Rule and Effective Nuclear Charge and Shielding.

Once $d$ starts filling, the effective-nuclear-charge picture flips $3d$ below $4s$, so on ionisation the $ns$ electrons leave first. This "add-to-$s$-first but remove-from-$s$-first" split powers Variable Oxidation States of Transition Metals.

8. Colour and magnetism — why "partially filled $d$" matters

Two final consequences you'll meet, so you know why the address is worth reading:

• A partly filled $d$ has empty seats an electron can jump into by absorbing light — that jump is a $d$–$d$ transition, giving colour (Colour and d-d Transitions).
• Unpaired ↑ electrons make an atom respond to magnets (Magnetic Properties (spin-only formula)).

A full $d^{10}$ (like Zn) has no empty seats and no unpaired spins → no colour from $d$–$d$, not a typical transition metal. That is why the IUPAC definition insists on a partially filled $d$.

Prerequisite map

Equipment checklist

Self-test: cover the right side, answer, then reveal.