How big is a cloud?
An atom has no hard edge. Its electrons form a cloud that thins out gradually, like mist. So it is fair to ask whether "the size of an atom" means anything at all.
It does, and the sizes are surprisingly different. A caesium atom has a radius about 3.6 times that of a fluorine atom. That means its volume is about 48 times bigger: you could fit roughly 48 fluorine-sized spheres inside one caesium-sized sphere. Both are atoms of single elements, sitting in the same periodic table.
Here is the puzzle that makes this lecture worth reading. Chlorine has 17 protons and 17 electrons. Sodium has only 11 of each. Yet a chlorine atom is smaller than a sodium atom. More particles, smaller atom. By the end of this lecture, you will be able to explain that, and to predict the size order of almost any two atoms from where they sit in the table.
Measuring the size of something with no edge
Because the cloud has no edge, chemists measure size in a way that does not need one. They find the distance between the centres of two atoms joined together, and take half of it. For two identical atoms joined by a single covalent bond, that half-distance is called the covalent radius.
The unit is the picometre, pm. One picometre is m, a million-millionth of a metre. Atomic radii are mostly between about 30 and 250 pm.
Different books list different numbers for the "atomic radius" of the same element. Some measure metals as metals (the metallic radius) and non-metals in molecules (the covalent radius), and those two methods give quite different values. Even two tables of covalent radii can differ by 10 pm or more. So compare only numbers that come from the same table. In this lecture, every radius is a single-bond covalent radius from one published table (Pyykkö and Atsumi, 2009).
A tug-of-war inside every atom
The size of an atom is set by how strongly its outer electrons are pulled towards the nucleus. A stronger pull draws the cloud in, and the atom is smaller. Two things decide that pull.
The nuclear charge. Each proton adds one unit of positive charge. More protons pull harder.
Shielding. You met this in the lecture on ionisation energies. Electrons in inner shells sit between the nucleus and the outer electrons, and they cancel part of the nucleus's pull. Electrons in the same shell shield each other only a little, because they are at about the same distance from the nucleus.
A simple way to combine the two is the effective nuclear charge: roughly, the nuclear charge minus the number of inner electrons. For sodium, 11 − 10 = 1. The outer electron feels about the pull of a single proton. This is a rough model, not an exact calculation, but it predicts the trends correctly.
Across a period: the atoms shrink
Move across Period 3 from sodium to chlorine. At each step, one proton is added to the nucleus and one electron is added to the outer shell. No new shell is started. Every new electron goes into shell 3.
So the nuclear charge rises by one at each step, but the inner shells stay exactly the same: 10 inner electrons all the way. The effective nuclear charge rises from about 1 for sodium to about 7 for chlorine. The outer electrons are pulled in harder and harder, so the atoms get smaller.
That is it. That is the whole idea, and it solves the puzzle. Chlorine does have more protons and electrons than sodium. But its extra electrons are all in the same shell as sodium's outer electron, so they add almost no shielding. Its extra protons, though, all pull. More pull, same number of shells: a smaller atom.
Down a group: the atoms grow
Now move down Group 1, from lithium to caesium. At each step, a whole new shell is added. Lithium's outer electron is in shell 2. Caesium's is in shell 6.
The nuclear charge rises a lot, from 3 to 55. But the number of inner electrons rises almost as much, so the shielding nearly cancels it. In the simple model, the effective nuclear charge stays at about 1 for every Group 1 atom. Meanwhile, each new shell is further from the nucleus. Same pull, further away: the atoms get bigger.
Explore both trends below. Watch which number changes, and which stays almost the same.
Choose a direction, then move through the elements. The atom is drawn to scale. Watch the shells, the inner electrons and the effective nuclear charge.
The numbers behind the two trends (covalent radii, Pyykkö and Atsumi 2009). The effective charge is the number of protons minus the number of inner electrons.
| Atom | Shells | Inner electrons | Effective charge | Radius (pm) |
|---|---|---|---|---|
| Na | 3 | 10 | 1 | 155 |
| Mg | 3 | 10 | 2 | 139 |
| Si | 3 | 10 | 4 | 116 |
| Cl | 3 | 10 | 7 | 99 |
| Li | 2 | 2 | 1 | 133 |
| K | 4 | 18 | 1 | 196 |
| Cs | 6 | 54 | 1 | 232 |
Across Period 3, the shells stay at 3 and the effective charge rises, so the radius falls. Down Group 1, the effective charge stays at about 1 and the shells increase, so the radius rises.
Shielding increases a lot down Group 1. Does it also increase across Period 3, as more electrons are added?
Show the answer
Hardly at all. Across Period 3, every new electron goes into the same outer shell. Electrons in the same shell are at about the same distance from the nucleus, so they shield each other very little. The inner electrons stay at 10 from sodium to chlorine. That is why the extra protons win, and the atoms shrink. Shielding grows only when a new inner shell is filled, which happens going down a group.
Putting the two trends together
Atoms get smaller to the right and larger downwards. So the smallest atoms are at the top right of the periodic table, near fluorine, and the largest are at the bottom left, near caesium. If two atoms differ in both row and column, check whether the two trends agree. Potassium is below and to the left of chlorine, so both trends make potassium larger: 196 pm against 99 pm.
When the two trends pull in opposite directions, the rules alone cannot decide, and you need the data. Practise the clear cases below.
Each card names two atoms. Decide which one is larger, then place the card. Each card explains itself.
Each pair, the larger atom, and why (covalent radii in pm):
| Pair | Larger | Reason |
|---|---|---|
| Na or Mg | Na (155 vs 139) | same period, Na further left |
| Li or K | K (196 vs 133) | same group, K further down |
| F or Cl | Cl (99 vs 64) | same group, Cl further down |
| Mg or Ba | Ba (196 vs 139) | same group, Ba further down |
| Si or P | Si (116 vs 111) | same period, Si further left |
| O or S | S (103 vs 63) | same group, S further down |
| Cl or Na | Na (155 vs 99) | same period; more protons in Cl, no new shell |
| Ca or Mg | Ca (171 vs 139) | same group, Ca further down |
Worked examples
Arrange Na, Si and Cl in order of increasing atomic radius.
All three are in Period 3, so the radius decreases from left to right: Na (Group 1), then Si (Group 14), then Cl (Group 17). In order of increasing radius, start with the smallest: Cl < Si < Na.
Check with the data: Cl 99 pm, Si 116 pm, Na 155 pm. The order is correct.
Explain why the radius increases from fluorine to iodine in Group 17.
| Atom | Outer shell | Radius (pm) |
|---|---|---|
| F | 2 | 64 |
| Cl | 3 | 99 |
| Br | 4 | 114 |
| I | 5 | 133 |
Each step down adds a new shell, so the outer electrons are further from the nucleus. The nuclear charge rises too, but the extra inner electrons shield most of it. In the simple model, the effective charge stays at about 7 for every halogen. Same pull, further away: the radius increases.
An examiner wants three ideas in an answer like this: more shells, more shielding, and further from the nucleus, which together outweigh the larger nuclear charge.
Explain why a magnesium atom is larger than a chlorine atom, even though chlorine has more protons.
Both atoms are in Period 3, so their outer electrons are in the same shell, shell 3. Both have 10 inner electrons, so the shielding is about the same. Chlorine has 17 protons and magnesium has 12, so chlorine's effective nuclear charge is larger (about 7 against about 2). Chlorine's outer electrons are pulled closer to the nucleus. So chlorine is smaller: 99 pm against 139 pm for magnesium.
Three classic mistakes
More protons pull harder. Across a period, they make the atom smaller. An atom is only bigger when it has more shells. Ask "how many shells?" before you ask "how many particles?".
Sodium is often listed as 186 pm (its metallic radius) and chlorine as 99 pm (its covalent radius). Comparing those two makes sodium look nearly twice the size of chlorine. On one table of covalent radii, the ratio is 155 to 99. The trend is the same, but the numbers are only fair when they come from one table.
Across a period, the new electrons go into the same shell, and they shield each other very little. The inner electrons do not change. Shielding increases going down a group, when new inner shells appear.
Work each one on paper first. Open a hint only when you are stuck.
-
Arrange Al, Mg, S and Na in order of increasing atomic radius.
Hint 1
All four are in Period 3. Which is furthest to the right?
Hint 2
The order across Period 3 is Na, Mg, Al, Si, P, S, Cl.
Full answer
Increasing radius means smallest first, which is the furthest right: S < Al < Mg < Na. Check with the data: 103, 126, 139 and 155 pm.
-
Potassium has 8 more protons than sodium. Explain why potassium is the larger atom.
Hint 1
Compare the number of shells, and the number of inner electrons.
Hint 2
Sodium is 2, 8, 1 and potassium is 2, 8, 8, 1.
Full answer
Potassium has 4 shells and sodium has 3, so potassium's outer electron is further from the nucleus. Potassium also has 8 more inner electrons, which shield its outer electron from the 8 extra protons. The effective nuclear charge is about 1 for both. So the extra distance wins, and potassium is larger: 196 pm against 155 pm.
-
Use the simple model to estimate the effective nuclear charge for magnesium and for sulfur. Which atom should be smaller? Check with the data.
Hint 1
Effective charge ≈ protons − inner electrons. Both atoms have 10 inner electrons.
Hint 2
Magnesium has 12 protons and sulfur has 16.
Full answer
Magnesium: 12 − 10 = 2. Sulfur: 16 − 10 = 6. Sulfur's outer electrons feel a much stronger pull in the same shell, so sulfur should be smaller. The data agree: S is 103 pm and Mg is 139 pm.
-
In the table used in this lecture, potassium (Group 1, Period 4) and barium (Group 2, Period 6) both have a covalent radius of 196 pm. Use both trends to explain how two such different atoms can be the same size.
Hint 1
Compare their positions: is barium further right or left than potassium? Further up or down?
Hint 2
One trend makes barium smaller than potassium, and the other makes it larger.
Full answer
Barium is one group to the right of potassium, which on its own would make barium smaller (a larger effective charge in its outer shell, about 2 against about 1). But barium is two periods lower, with two more shells, which on its own would make it larger. Here the two effects happen to balance, so the radii are equal. This is why "diagonal" comparisons need data: the rules point in opposite directions, and only measurement can say which wins.
Almost every trend in the periodic table comes back to the same tug-of-war: how strongly the nucleus pulls on the outer electrons, against how far away they are and how well they are shielded. Atomic radius is the most visible result of that contest.
The same contest explains why a large atom like caesium loses its outer electron so easily, and why a small atom like fluorine pulls electrons towards itself so strongly. The next lectures follow this one idea through ionisation energy, electronegativity and reactivity.
- Because an atom has no edge, its size is measured as half the distance between the nuclei of two bonded identical atoms, and radii should be compared only within one table.
- The effective nuclear charge, roughly the number of protons minus the number of inner electrons, measures how strongly the outer electrons are pulled.
- Across a period, protons are added but no new shell is started, so the effective nuclear charge rises and the atoms get smaller.
- Down a group, each step adds a shell further from the nucleus while extra shielding keeps the effective charge about the same, so the atoms get larger.
- More protons alone does not make an atom bigger; more shells does.