Analyze atomic radius, ionization energy, electronegativity, and ionic radius across periods and groups using effective nuclear charge and shielding.
A lesson of Chemistry, in Atomic Structure and Periodicity, about 40 minutes.
By the end of this lesson, you will be able to explain every major trend using effective nuclear charge and shielding, compare any two elements, and predict how an ion's size differs from its atom's.
One Idea Explains All of Them
$$Z_{\text{eff}} = Z - S$$
Effective nuclear charge is how much positive pull an outer electron actually
feels: the full nuclear charge $Z$, minus the shielding $S$ from the inner
electrons that sit between.
Every trend in this lesson is that one quantity changing.
Across a period, $Z_{\text{eff}}$ INCREASES. Protons are added one at a time,
but the new electrons go into the SAME level, so they shield each other very
poorly. The pull grows and the shielding barely changes.
Down a group, $Z_{\text{eff}}$ stays roughly constant while a whole new energy
level is added. Each new inner shell shields almost perfectly, canceling out the
extra protons, so what changes is distance rather than pull.
Hold those two sentences and the rest of the lesson is derivation rather than
memorization.
Atomic Radius
Decreases across a period. Rising $Z_{\text{eff}}$ pulls the same outer level
inward, so atoms get smaller left to right, which surprises people who expect
more electrons to mean a bigger atom.
Increases down a group. Each period adds an energy level further from the
nucleus, and distance beats everything else.
$$\text{largest: bottom left} \qquad \text{smallest: top right}$$
Francium is the biggest atom; helium is the smallest.
Down beats across when the two conflict, because adding a whole energy level
is a bigger change than adding one proton. Comparing potassium and chlorine,
potassium is larger despite being further right in its own period, since it is a
period below.
Sort It: Which Atom Is Larger
Example 1: Comparing Two Atoms
Here is every step, worked all the way through.
Which is larger, sodium or chlorine?
Which period is sodium in? 3
Chlorine is in the same period. What is the difference between their period numbers? 0
Same period, so compare left to right. Which is further LEFT? Type the symbol Na
Across a period, does the radius increase or decrease? Type one word decrease
The energy needed to remove an outer electron. It runs opposite to radius,
which follows directly: a tightly held, close-in electron is hard to remove.
Increases across a period (higher $Z_{\text{eff}}$, tighter grip).
Decreases down a group (the outer electron is further away and better
shielded).
$$\text{highest: top right} \qquad \text{lowest: bottom left}$$
Helium is hardest, francium easiest, and that is why francium is the most reactive
metal and helium the most inert element.
The trend across a period has two small dips, and they are evidence rather
than noise:
Group $13$ dips because its outermost electron is a $p$ electron, which is
higher in energy than the $s$ electrons below it and easier to remove
Group $16$ dips because its fourth $p$ electron is forced to pair up in an
already-occupied orbital, and the repulsion makes it easier to remove
Those two exceptions are direct confirmation of the orbital picture from the
previous lesson. A simple "charge increases across" model predicts a smooth rise
and cannot explain them.
Successive Ionization Energies
Removing a SECOND electron always costs more than the first, because you are
pulling a negative particle away from an ion that is already positive.
But the jump is not gradual. It leaps enormously when you break into a full
inner level.
The third electron costs five times the second, because magnesium's first two
electrons are its valence electrons and the third has to come out of a complete
neon core.
The position of the huge jump tells you the group number, which is a genuinely
useful diagnostic: an element whose fourth ionization energy leaps has three
valence electrons and is in group $13$.
Worked Example 1: Reading a Jump
An element's successive ionization energies are $578$, $1817$, $2745$,
$\mathbf{11577}$ kJ/mol.
Electronegativity
How strongly an atom pulls on the electrons in a BOND it is part of. This is
about shared electrons, not about removing them, which is what distinguishes it
from ionization energy.
Increases across a period, decreases down a group, the same directions as
ionization energy and for the same $Z_{\text{eff}}$ reason.
Those boundaries are conventions, not physics. Bonding is a continuum from
pure sharing to complete transfer, and $1.7$ is a useful line drawn across it
rather than a real edge.
Sort It: Bond Type From the Difference
Ionic Radius
Ions are not the same size as their atoms, and the direction of change is
predictable.
Cations are SMALLER than their atoms. Losing electrons often empties the
entire outer level, so the remaining electrons sit in a level closer in, and the
unchanged nuclear charge now pulls fewer electrons more tightly.
Nearly half the size, because sodium's single $3s$ electron was its whole outer
level.
Anions are LARGER than their atoms. Added electrons increase repulsion among
the outer electrons while the nuclear charge stays the same, so the cloud
expands.
All ten electrons. More protons means a smaller ion, with nothing else
varying, which is about as clean a demonstration of $Z_{\text{eff}}$ as chemistry
offers.
Worked Example 2: Ion Sizes
Worked Example 3: Using the Trends Together
Compare potassium and bromine.
Common Mistakes
Mistake 1: Expecting atoms to grow across a period
More electrons, but a stronger pull. They shrink.
Mistake 2: Getting ionization energy backwards
It runs OPPOSITE to radius. Small atom, tight grip, high energy.
Mistake 3: Confusing electronegativity with ionization energy
One is pull within a bond, the other is the cost of removal.
Mistake 4: Thinking cations are bigger because they are charged
They lost a whole level, so they are smaller.
Mistake 5: Treating $1.7$ as a hard boundary
Bond character is a continuum; the number is a convention.
Where This Goes Next
Periodic trends are how chemistry becomes predictive rather than encyclopaedic.
Given two elements you have never met, their positions give you the bond type,
the likely formula, whether the compound conducts when molten, roughly how
reactive it is, and whether it will dissolve in water. That is a great deal from
a seating plan, and it is why Mendeleev could describe germanium before anyone
had seen it.
The trends also explain the shape of the world. Fluorine's extreme
electronegativity makes $\mathrm{C\text{-}F}$ bonds the strongest in organic
chemistry, which is why Teflon is inert and why some fluorinated compounds persist
in the environment for centuries. Cesium's minuscule ionization energy makes it
release electrons when struck by light, which is what photoelectric cells use.
At the very bottom of the table, relativity intervenes. In heavy atoms the inner
electrons move fast enough for relativistic effects to matter, contracting the $s$
orbitals. That is why gold is yellow rather than silver-colored, and why mercury
is liquid at room temperature: two of the most familiar properties of two of the
most familiar metals come from Einstein rather than from the trends above.
Trends are a first approximation, and a very good one. The exceptions are where
the physics gets interesting.
Check Your Understanding
Five of them, no instructions this time.
Summary
$$Z_{\text{eff}} = Z - S$$
Across a period the pull increases; down a group the distance increases. Every
trend is one of those two.
Radius shrinks across and grows down. Ionization energy and electronegativity
do the opposite of radius.
A huge jump in successive ionization energies marks the end of the valence
electrons, and its position gives the group.
Electronegativity DIFFERENCE predicts the bond type, on a continuum rather
than at a hard boundary.
Cations shrink, anions grow, and within an isoelectronic series more protons
means smaller.