Write electron configurations and orbital diagrams using Aufbau, Pauli exclusion, and Hund rules. Connect valence electrons to chemical reactivity.
A lesson of Chemistry, in Atomic Structure and Periodicity, about 35 minutes.
By the end of this lesson, you will be able to write a configuration using the three filling rules, draw an orbital diagram, count valence electrons, and read a configuration straight off the periodic table.
Orbitals: Where an Electron Probably Is
An electron does not orbit like a planet. It occupies an orbital, a region
where it is likely to be found, and each orbital holds at most two electrons.
Sublevel
Orbitals
Max electrons
Shape
$s$
$1$
$2$
sphere
$p$
$3$
$6$
dumbbells on three axes
$d$
$5$
$10$
four-lobed, mostly
$f$
$7$
$14$
complicated
Two per orbital, always, so the maximums are just twice the orbital count.
Energy levels are numbered $n = 1, 2, 3, \ldots$, and level $n$ contains $n$ kinds
of sublevel: level $1$ has only $s$, level $2$ has $s$ and $p$, level $3$ has $s$,
$p$ and $d$.
Aufbau: lowest energy first. Electrons fill the cheapest available seat.
Pauli exclusion: two per orbital, opposite spins. No two electrons in an atom
can be identical in every respect, so the two sharing an orbital must differ in
spin.
Hund: spread out before pairing. Within a sublevel, put one electron in each
orbital before doubling any up, and keep those unpaired spins parallel.
Hund's rule has a physical reason: electrons repel, so two of them in
different $p$ orbitals sit further apart and the arrangement costs less energy
than crowding them into one.
Replace the filled inner levels with the noble gas that has exactly that
configuration, in square brackets.
Find the noble gas in the period ABOVE, then write what comes after it.
Sulfur is in period $3$, so the shorthand starts from neon at the end of period
$2$.
$$\text{iron} = [\mathrm{Ar}],4s^2 3d^6$$
This is not laziness; it is emphasis. The inner electrons are chemically
inert, and everything that matters chemically is what the brackets leave visible.
Writing iron's twenty-six electrons out in full buries the eight that do anything.
Valence Electrons Decide the Chemistry
Valence electrons are the outermost-level electrons, and they are the ones
that bond, transfer or get shared. Everything about an element's chemical
behavior comes from them.
Count everything in the highest $n$ level: $3s^2$ and $3p^4$ give $6$.
For main-group elements, the group number gives it directly. Group $1$ has
one, group $2$ has two, groups $13$ to $18$ have $3$ through $8$. Sulfur is in
group $16$, and $16 - 10 = 6$.
Elements in the same group have the same valence count, which is why they
behave alike, and that single fact is what the periodic table is organized
around. Lithium, sodium and potassium all have one valence electron and all react
violently with water for the same reason.
$d$ electrons are not valence electrons in the counting sense, which is why
iron's $[\mathrm{Ar}]4s^2 3d^6$ has two valence electrons rather than eight, even
though the $d$ electrons do participate in transition-metal bonding.
Worked Example 1: Shorthand and Valence
Calcium, atomic number $20$.
Orbital Diagrams
A configuration says how many; an orbital diagram says how they are arranged, and
that is what reveals unpaired electrons.
The fourth electron has to pair up, leaving two unpaired, and oxygen forms two
bonds.
Unpaired electrons are why some substances are magnetic. Oxygen gas is drawn
toward a magnet because of those two unpaired electrons, and liquid oxygen
visibly sticks to a magnet's poles. A configuration alone would not have
predicted that; the diagram does.
Worked Example 2: An Orbital Diagram
Oxygen, atomic number $8$.
Reading It Off the Table
The periodic table is a configuration chart, and once you see that, nothing needs
memorizing.
Groups $1$ and $2$ are the $s$-block, two columns wide
Groups $13$ to $18$ are the $p$-block, six columns wide
Groups $3$ to $12$ are the $d$-block, ten columns wide
The two rows below are the $f$-block, fourteen columns wide
The block widths ARE the sublevel capacities: $2$, $6$, $10$, $14$. That is
not a coincidence; it is the reason the table has the shape it has.
The period number gives the level, with two adjustments: $d$ electrons are one
level behind the period, and $f$ electrons are two behind. Iron is in period $4$
and its $d$ electrons are $3d$.
$$\text{find the element, read left to right along the periods}$$
Bromine sits in period $4$, $p$-block, fifth column of it, so its configuration
ends $4p^5$, and the shorthand is $[\mathrm{Ar}]4s^2 3d^{10} 4p^5$.
Worked Example 3: From the Table
Bromine, atomic number $35$.
Common Mistakes
Mistake 1: Filling $3d$ before $4s$
$4s$ is lower in energy and fills first.
Mistake 2: Pairing before spreading
Hund's rule: one electron in each orbital of a sublevel first.
Mistake 3: Superscripts that do not add to the atomic number
Always check the total.
Mistake 4: Counting $d$ electrons as valence
Iron has two valence electrons, not eight.
Mistake 5: Wrong noble gas in the shorthand
Use the one ending the period ABOVE.
Where This Goes Next
The rules in this lesson are approximations, and they have known exceptions worth
seeing rather than hiding.
A half-filled or completely filled $d$ sublevel is unusually stable, so an
electron is promoted out of $4s$ to achieve it. The Aufbau order is a rule of
thumb about energies that are very close together, not a law, and when two
arrangements are nearly equal in cost, small effects decide.
Underneath, the real object is the Schrödinger equation, and the orbitals are
its solutions. It is solved exactly only for hydrogen; every other atom requires
approximation, because the electrons repel each other and the problem has no
closed form. The $s$, $p$, $d$ and $f$ labels are quantum numbers falling out of
that mathematics, and their shapes are three-dimensional standing waves.
The payoff is immediate. Everything the next two lessons say about the periodic
table, and everything the bonding unit says about how atoms combine, follows from
where the electrons sit. The table was arranged by chemical behavior decades
before anyone knew about orbitals, and configuration explained why the
arrangement worked.
Check Your Understanding
Five of them, no instructions this time.
Summary
Two electrons per orbital, with $s$, $p$, $d$ and $f$ holding $2$, $6$, $10$
and $14$.
Three rules: lowest energy first, two per orbital with opposite spins, and
spread out before pairing. $4s$ fills before $3d$.
Check the superscripts add to the atomic number.
Valence electrons are the outermost level, they decide all the chemistry, and
the group number gives them for main-group elements.
The periodic table IS a configuration chart, and the block widths are the
sublevel capacities.