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Trends across a period and down a group

Atomic radius, ionization energy and electronegativity as three ways of asking one question, and the exceptions that show the answer is right.

Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.

1. What you will learn

By the end of this lesson you will be able to rank elements by atomic radius, first ionization energy and electronegativity from their positions alone, and — separately — to say what causes each trend, which is the part that survives an exception. You will be able to explain the two dips that break the ionization-energy climb in every period.

2. What you already have

You can place an element from its electron arrangement and read a position back as a count of outer electrons and a count of shells. This lesson takes that one step further: if you know where two elements are, you can say which of them has the larger atom, which holds its outer electron more tightly, and which pulls harder on a pair of electrons it is sharing — without having met either of them before.

3. Words for this lesson

4. Measurements first, reasons after

Nobody decided these numbers. They were measured, and the rest of this lesson was written to fit them.

First ionization energy in kJ/mol and atomic radius in picometers, across period 2:

and down group 1:

Which way does each go, across a period and down a group? Do the two agree — if an atom is smaller, is its electron easier or harder to remove? And one cause or two? Two things change as you move: how many protons pull, and how many shells stand in the way.

Then the exceptions. Boron's ionization energy is lower than beryllium's, and oxygen's is lower than nitrogen's — two dips in a climb. A rule with exceptions is either wrong or incomplete; decide which, and what would settle it.

5. Three trends, two causes

A trend across the periodic table is a consequence and not a rule. Two things move as you cross a period: the charge on the nucleus goes up, and the electrons being added go into the same shell, so they shield each other hardly at all. Every trend in this unit follows from those two sentences, and the exceptions follow from them too — which is why the exceptions are worth knowing rather than worth memorising.

There are only two things that change as you move through the table, and every trend is one of them.

Across a period, left to right. Each step adds one proton to the nucleus and one electron to the shell that is already in use. An electron in the same shell as another shields it hardly at all, so the pull on the whole outer shell grows and its distance from the nucleus does not. The shell is dragged in.

Down a group. Each step adds a whole new shell. The outer electrons are now one shell further out, and every filled shell beneath them stands between them and the nucleus. The pull on them weakens.

Now read the three properties off those two sentences.

All three are the same question asked three ways: how hard is this nucleus holding the outer electrons? That is why they move together, and why learning one of them is close to learning all three.

6. The method, step by step, and how to check it

Place the elements. Find each element's period and group.

Decide the direction. Same period means the comparison runs across a row; same group means it runs down a column.

Apply the cause. Across a period, more protons pull on the same shell. Down a group, the outer shell is further out and better shielded.

Read off the property. Smaller radius, higher ionization energy and higher electronegativity all go with a tighter hold.

Order them as the question asks. Read again which end it wants first.

Check the work. Does the ranking agree across the three properties — is the smallest atom also the one with the highest ionization energy? If two of the elements are a pair known to break the climb, such as magnesium and aluminum, have you allowed for the dip? And for any measured values given, do the differences you worked out have the sign the trend predicts?

7. Why each step is allowed

Reasoning from charge and distance is allowed because an electron is held by electrical attraction to the nucleus, and that attraction grows with the charge pulling and weakens with the distance between them.

Treating electrons in the same shell as hardly shielding each other is allowed because they are, on average, the same distance from the nucleus. One does not sit between the nucleus and another, so it cannot screen it much.

Treating a filled inner shell as strong shielding is allowed because those electrons lie between the nucleus and the outer ones. Their negative charge cancels much of the nucleus's pull, so the outer electrons feel a far smaller effective charge than the full count of protons.

Accepting the dips as part of the model is allowed because the same two causes, applied to sub-levels and orbitals rather than whole shells, predict exactly where they fall. A model is tested by whether it explains the awkward cases, and this one does.

8. The exceptions, and why they are the best evidence

First ionization energy climbs across a period — except in two places, and the same two places in every period.

You have already found them in the period 2 figures: boron at 801 below beryllium at 900, and oxygen at 1314 below nitrogen at 1402. Period 3 dips in the same two positions: aluminum at 578 below magnesium at 738, and sulfur at 1000 below phosphorus at 1012.

The first dip. Beryllium's two outer electrons fill a sub-level. Boron's extra electron has nowhere to go but the next sub-level up, which sits a little further from the nucleus — so it comes away a little more easily, in spite of boron having one more proton. Aluminum does the same thing to magnesium one period lower.

The second dip. Nitrogen has three electrons in three separate orbitals, one each. Oxygen has four in three orbitals, so two of them are crowded into one. Two electrons in one orbital repel each other, and that repulsion helps one of them leave — so oxygen's first electron is easier to remove than nitrogen's. Sulfur does the same thing to phosphorus.

If the climb were a rule, these four would be four things to remember. Because it is a consequence of nuclear charge and distance, the dips are the same model at finer grain — and a model that predicts its own exceptions beats one with none.

9. Where a trend stops being a trend

Two cautions about reading too much into a number.

A trend compares; it does not measure. Electronegativity has no unit. The Pauling scale sets fluorine at 4.0 and places everything else relative to it, so the differences are what mean something: 0.1 between two elements is not worth acting on, and 2.0 is the difference between sharing electrons and handing one over.

The transition metals do not follow the period trend. Crossing the middle trough, the electrons being added go into the shell beneath the outer one, so the outer shell barely changes and neither do the properties. Iron, cobalt and nickel are far more alike than sodium, magnesium and aluminum. That is not the trend failing; it is the trend's cause being absent, which is what the cause predicts.

10. In the world: why lithium powers American cars

Every electric car built at the Tesla plant near Reno, Nevada runs on lithium, and the periodic trends explain the choice. A battery stores energy by moving metal ions between two electrodes, so the ideal metal gives up its outer electron easily, is light, and has small ions that move quickly.

Group 1 metals all give up their single outer electron readily, which is why they are the obvious family to look in. Within the group, the trends pull in two directions. Down the group, ionization energy falls — from 520 kJ/mol for lithium to 419 for potassium — so the lower metals give up their electrons even more easily. But the atoms also grow, from 152 picometers for lithium to 227 for potassium, and they get heavier.

Lithium wins on size and weight: the smallest and lightest metal in the group packs the most stored energy into each pound of battery, which matters in a car. Sodium, one row down, is larger and heavier but far cheaper and more plentiful, so labs in Michigan and elsewhere are developing sodium-ion batteries for grid storage, where weight matters less than cost. The same two trends, read for different priorities, give two different choices.

11. In the world: why fluorine compounds coat pans

Nonstick pans are coated with a polymer of carbon and fluorine. Fluorine is the most electronegative element, so it holds its electrons so tightly that almost nothing — water, oil, food — can bond to the surface.

12. Where this goes wrong

The trend is memorized as an arrow and applied blind. A learner who knows only that ionization energy "goes up across a period" will put aluminum above magnesium and be wrong. The arrow is the summary; the nuclear charge and the distance are the reason, and the reason is what survives the exceptions.

Mass is taken as the cause. Heavier atoms are said to hold electrons more tightly. Mass is in the nucleus and does nothing to an electron; what holds an electron is the electrical pull of the protons, weakened by distance and by the shells in the way. Cesium is one of the heaviest ordinary metals and gives its outer electron up more readily than almost anything else.

Shielding is forgotten going down a group. The nuclear charge rises steeply down a group — potassium has nineteen protons to lithium's three — so a learner reasoning from charge alone predicts the opposite of what happens. The extra shells outweigh the extra charge, every time.

Electronegativity is read as a measurement with a unit. It is a comparison on a made scale, and its numbers are only worth anything as differences.

The question's direction is not read. "Largest first" and "smallest first" are different answers to the same chemistry, and the family grades what was asked for.

13. Ranking three elements by atomic radius

1. Place the three elements.

   $\text{sodium, silicon, chlorine: all period } 3$

   Decide the direction before ranking anything.

2. Decide the direction.

   $\text{across a period}$

   All three have three shells.

3. Count the protons pulling.

   $11, \ 14, \ 17$

   More pull on the same shell.

4. Apply the cause.

   $\text{more protons} \Rightarrow \text{smaller atom}$

   The shell is dragged in.

5. Write the order, smallest first.

   $\text{chlorine, silicon, sodium}$

   The atom with the most protons is the smallest.

14. Explaining a dip rather than remembering it

1. Read the first three values.

   $\text{Na } 496, \ \text{Mg } 738, \ \text{Al } 578$

   First ionization energies, kJ/mol.

2. Find the first change.

   $738 - 496 = 242$

   The climb continues.

3. Find the second change.

   $578 - 738 = -160$

   The climb breaks at aluminum.

4. Find magnesium's sub-level.

   $\text{two outer electrons fill one sub-level}$

   The last one goes in close.

5. Find aluminum's new electron.

   $\text{it starts the next sub-level}$

   A little further out, so easier to remove.

6. Check that the climb resumes.

   $\text{Si } 787 > 578$

   One dip, one reason, and the trend continues.

15. Ranking down a group, and checking against the numbers

1. Place the three elements.

   $\text{lithium, sodium, potassium: group } 1$

   Same column.

2. Decide the direction.

   $\text{down a group}$

   One more shell at each step.

3. Apply the cause.

   $\text{further out, more shielded}$

   The outer electron is held less tightly.

4. Predict the ionization energy order, highest first.

   $\text{lithium, sodium, potassium}$

   The weakest hold gives the lowest energy.

5. Read the measured values.

   $520, \ 496, \ 419$

   In kJ/mol.

6. Check the steps.

   $496 - 520 = -24; \ 419 - 496 = -77$

   Both negative: the energy falls down the group.

7. Predict the reactivity.

   $\text{potassium reacts hardest}$

   Its outer electron comes away most easily.

16. Your turn: rank fluorine, chlorine and bromine by first ionization energy, lowest first.

1. Decide the direction.

   $\text{all group } 7: \text{ down a group}$

   Same column, different number of shells.

2. Apply the cause.

   $\text{further out and shielded} \Rightarrow \text{easier}$

   Each lower element has one more shell.

3. Your turn: work this step out. Its working is at the end of the packet.

   Write the order, lowest first.

17. Guided practice

Here are three elements: carbon, fluorine and lithium. For these three, all three are in period 2. Put them in order of atomic radius, smallest first.

Number the steps in order (write the number in the box):

• fluorine
• carbon
• lithium

18. Guided practice

Complete the worked solution: first ionization energies in kilojoules per mole are magnesium $738$, aluminum $578$ and silicon $787$. Find the change from magnesium to aluminum, from aluminum to silicon, and from magnesium to silicon.

1. Find the change from magnesium to aluminum.

   $(\text{aluminum}) - (\text{magnesium}) =$ _a

   Negative: the climb breaks at aluminum.

2. Find the change from aluminum to silicon.

   $(\text{silicon}) - (\text{aluminum}) =$ _b

   Positive: the climb resumes.

3. Find the change across all three.

   $(\text{silicon}) - (\text{magnesium}) =$ _c

   Overall, the energy still rises across the period.

19. Guided practice

For chlorine, sodium and silicon, all three are in period 3, and their electronegativity changes steadily along that direction. Which sentence explains why?

• Across the period the nucleus gains a proton at every step while the new electrons enter the shell that is already in use, so the pull on the outer shell grows stronger.
• Down the group each element has one more filled shell, so the outer electrons sit further out and are screened from the nucleus by the shells in between.
• The atoms get heavier, and a heavier atom holds on to its electrons more tightly.
• The elements were arranged in this order because of the trend, so the order is what makes the trend true.

20. Guided practice

Here are three elements: chlorine, fluorine and bromine. For these three, all three are in group 7, the halogens. Put them in order of electronegativity — how hard the atom pulls on a pair of electrons it is sharing — with the **strongest puller first** this time.

Number the steps in order (write the number in the box):

• bromine
• chlorine
• fluorine

21. Practice

The first ionization energy of lithium is $520$ kJ/mol and that of rubidium, further down group 1, is $403$ kJ/mol. How many kilojoules per mole less does it take to remove rubidium's outer electron?

Answer:

22. Practice

A battery lab in Michigan is comparing group 1 metals for a cheaper battery, and size matters because larger atoms move through the electrode more slowly. The atomic radius of lithium is $152$ pm and of potassium is $227$ pm. How many picometers larger is a potassium atom?

The answer: _a.

23. Somewhere new

A works is testing a new surface coating and needs to know which end of a bond carries the small negative charge, because that is the end water will cling to. The bond joins an atom of beryllium to an atom of oxygen, and the pair of electrons between them does not sit halfway: it sits closer to whichever atom pulls harder. Which atom is that?

• beryllium
• oxygen
• Neither: a pair of electrons shared between two atoms is always shared equally.
• Whichever atom is larger, because a larger atom has more electrons and so more pull.

24. Lesson test

Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.

25. Test question

These are five consecutive elements at the start of period 3, with their first ionization energies in kilojoules per mole: sodium $496$, magnesium $738$, aluminum $578$, silicon $787$, phosphorus $1012$. For each step along the row, give the change in kilojoules per mole — negative where the value falls — and say whether that step breaks the general climb.

26. What you can do now

You can rank three elements on any of the three trends and give the cause rather than the arrow. Say out loud why aluminum's first ionization energy is lower than magnesium's when aluminum has one more proton. Next: what atoms do with their outer electrons when they meet — ionic bonding, and the formula that falls out of the charges.

Working for the steps left to you

16. Your turn: rank fluorine, chlorine and bromine by first ionization energy, lowest first., step 3