The Periodic Table
Everybody is handed this chart and told to learn it. Almost nobody is told that it was not designed. It came out of an experiment โ and then, fifty years later, out of an argument about where electrons go.
You are going to build it. Not copy it: build it, twice. Once the way Mendeleev did, by shuffling cards until a pattern falls out. Then again from the electrons up, until the eighteen columns are not something you remember but something you could not have avoided.
Nothing is asserted
Every configuration on this site is built by the filling order as you watch, and every period, group, block and valence count is read back off it. The element data holds only what somebody actually had to measure.
The trainer cannot be memorised
Fifteen generators, every question made on the spot and dealt from a shuffled deck. Sit the mock paper ten times and you will not meet the same paper twice.
It tells you what to fix
Every question is tagged with the section that teaches it, so the end of a mock paper is not a score โ it is a list of what to reread, weakest first, with a button that takes you there.
Getting around
Arrow keys move between sections. Everything you do is saved in this browser, so you can close the tab and come back. The ๐จ button prints the whole lesson, and section 16 is a one-page reference built for exactly that.
Sixty-three elements, no order
In 1869 a chemist in St Petersburg had sixty-three elements, a list of their masses, a list of their properties, and no idea how any of it fitted together. He wrote each one on a card and started dealing.
Try to see the problem as it looked then. Sodium is a soft metal that catches fire in water. Chlorine is a green gas that kills. Put them together and you get table salt. Nobody knew why. There were elements that behaved almost identically โ lithium, sodium and potassium could stand in for one another in almost any reaction โ and elements next door to each other on any list you could make that had nothing whatever in common.
Dmitri Mendeleev's idea was to lay the cards out in order of atomic mass, which was the only number anyone could measure reliably, and then start a new row whenever the properties came back round. The question is: how long is the row?
๐ Deal the cards yourself
0 / 5Here are the 17 lightest elements, in order of atomic mass, wrapped onto a new row every so often. Change the row length until every column becomes a chemical family. Then switch the noble gases on and find the answer again โ and when that does not work either, you will have found the thing section 02 is about.
Why seven and not eight?
With the noble gases hidden the repeat is seven, and that is genuinely what Mendeleev's table looked like โ because argon was not discovered until 1894, twenty five years later, and the whole family was missing. When they turned up they did not break the table. They slotted in as a new column on the end and turned every seven into an eight. A pattern that survives the discovery of a whole family it never accounted for is a pattern that was real.
And then eight does not work either
Switch the noble gases on and set the row length to eight, and two columns still refuse to line up. That is not a mistake in the puzzle โ it is a mistake in the ordering rule. Argon is heavier than potassium but has one proton fewer, so sorting by mass puts it on the wrong side and drags a whole row out of position. Change the last control from mass to atomic number and the table snaps into place. Nobody could justify that switch in 1869. Section 02 is about the man who could.
The part that made it a theory
Sorting is not science. What made Mendeleev's table more than a filing system is that he left gaps โ and then said what would be found in them. Where the pattern demanded an element that nobody had, he refused to close the gap and predicted the missing element's properties from its neighbours instead.
| Property | Predicted 1871 โ "eka-silicon" | Measured 1886 โ germanium |
|---|---|---|
| Atomic mass | 72 | 72.6 |
| Density | 5.5 g/cmยณ | 5.35 g/cmยณ |
| Oxide | EsOโ, density 4.7 | GeOโ, density 4.7 |
| Chloride | EsClโ, boils below 100 ยฐC, density 1.9 | GeClโ, boils at 86 ยฐC, density 1.88 |
| Appearance | Dark grey metal | Greyish-white metalloid |
Fifteen years apart, and to two significant figures. He did the same for gallium and scandium, and was right about both. That is what turned an arrangement into a law: it said something about elements that did not yet exist, and it turned out to be true.
But the rule was wrong
Three times, Mendeleev had to break his own ordering rule to keep a family together โ putting a heavier element before a lighter one because the chemistry demanded it. He never knew why. Section 02 is about the man who found out, and who died at Gallipoli two years later, aged twenty-seven.
The number that fixed it
Atomic mass is nearly right, and nearly right is the worst thing a rule can be. In 1913 Henry Moseley measured something else instead โ and the something else was exact.
Moseley fired high-energy electrons at metal targets and measured the wavelength of the X-rays that came back out. He found that the square root of the frequency went up in clean, evenly spaced steps as he worked along the elements โ and the step size was one. Not one unit of mass. One proton.
Moseley's law. Z is the number of protons โ and it is a whole number, with no gaps and no fractions, which is exactly what an ordering rule needs to be.
๐ Order by mass, or order by protons
Three pairs of elements are in the wrong order if you sort by mass. Flip the switch and watch them swap โ then look at what happens to Moseley's measurement underneath.
๐ What Moseley actually measured
Twelve elements, their measured X-ray wavelengths turned into โfrequency, plotted against whichever ordering rule is selected above.
Neutrons come along for the ride
Add a proton and you almost always add a neutron or two as well, so mass climbs roughly in step with charge. That is why Mendeleev's rule worked for sixty elements out of sixty-three. It fails wherever an element happens to have an unusually heavy mix of isotopes โ tellurium's common isotopes are heavy, iodine's are light, and the two cross over.
Everything downstream depends on it
Z is the number of protons, which is the number of electrons in a neutral atom, which is what the next four sections spend their time arranging. If the table were ordered by mass, the electron count would not run in step with the position and none of the patterns in this lesson would exist.
Shells, subshells, orbitals
Three words that get used as if they meant the same thing. They do not, and the difference between them is what gives the table its shape โ so it is worth ten minutes.
Shell
A whole energy level, numbered n = 1, 2, 3โฆ Roughly, how far out the electrons are. The period number of an element is the number of its outermost shell.
Subshell
A shell splits into n subshells, labelled s, p, d, f. They differ in shape and slightly in energy. The subshell being filled names the block.
Orbital
A subshell contains orbitals โ the actual regions an electron occupies. An orbital holds two electrons and never more. Think of it as a two-seat bench.
๐ช Fill a subshell and watch the rules take over
Hund's rulePick a subshell, then drag electrons into it one at a time. Nothing here is a convention โ every arrangement is the lowest-energy one available, and the commentary names the rule that is deciding at that moment.
Pauli exclusion principle
No two electrons in one atom can have all four quantum numbers the same. In practice: an orbital holds at most two electrons, and if it holds two their spins must be opposite. There is no third seat and no arguing about it.
Hund's rule
Within a subshell, every orbital gets one electron before any orbital gets a second โ and those single electrons all spin the same way. Electrons repel, so they spread out. Everyone sits alone on the bus before anyone shares a seat.
The arithmetic of a shell
Shell n contains n subshells. Those subshells contain nยฒ orbitals between them, and each orbital holds two electrons โ so shell n holds 2nยฒ electrons. Every number in the table below is computed from the boxes above it.
| Shell | Subshells | How many | Orbitals | Electrons |
|---|
The four numbers to carry forward
s = 2 ยท p = 6 ยท d = 10 ยท f = 14. Learn these four and you have already learnt the width of every block in the periodic table, the length of every period, and why there are eighteen columns. Section 05 does nothing but cash that in.
The Aufbau machine
One list, nineteen entries, and it generates the electron configuration of every element that exists. This is the single most useful thing in the topic.
Aufbau is German for building up, and the principle is exactly as obvious as it sounds: electrons go into the lowest-energy space available. The only hard part is that the energy order is not the shell order. The 4s subshell is lower in energy than 3d, so it fills first โ which is why potassium and calcium are ordinary metals in period 4 and the transition metals only start afterwards.
The diagonal rule, stated properly. โ is 0 for s, 1 for p, 2 for d, 3 for f. So 4s (4 + 0 = 4) comes before 3d (3 + 2 = 5), and 3d before 4p (4 + 1 = 5, but higher n).
โ๏ธ Build any element
Z = 26Drag the slider, use the arrows, or click a cell on the little table. Watch the ladder fill in the order the diagonal rule dictates, and watch the same configuration appear two different ways underneath.
The filling order
Filling order is not writing order
Iron is built โฆ 4sยฒ 3dโถ and written โฆ 3dโถ 4sยฒ. Both are
correct, and both earn the mark โ but they are answers to different questions. Build
in energy order, write in shell order. This is also the reason iron loses its 4s
electrons first when it forms an ion, which is section 12 and the single most
commonly dropped mark in the whole topic.
Why the table looks like that
Two columns, then six, then ten, then fourteen. Nobody chose those numbers. They are the four subshell capacities from section 03, and they are the whole explanation for the shape of the periodic table.
๐งฑ Switch the blocks on
18 columns ยท 118 elementsTurn each block on and watch the table get wider by exactly the capacity of that subshell. Or press Build and watch it assemble itself.
This is the honest table
The f block belongs here โ between group 2 and group 3 โ because that is where the filling order puts it. It is normally drawn as a strip underneath for one reason only: thirty-two columns do not fit on a page or a classroom wall. It is a printing decision, not a chemical one, and it is worth seeing the real shape once so that the strip stops looking arbitrary.
Where each width comes from
Where each period length comes from
A period runs from one s subshell to the next noble gas. Its length is just the total capacity of everything that fills along the way โ which is why the lengths go 2, 8, 8, 18, 18, 32, 32 and not 2, 4, 6, 8 as a naive guess would have it.
| Period | Subshells filling | Capacities | Length | Ends at |
|---|
Why do periods 2 and 3 have the same length?
Because the third shell's d subshell does not fill during period 3. 3d sits above 4s in energy, so period 3 runs 3s then 3p and stops at argon after eight elements โ and the 3d subshell waits for period 4. The same thing happens with 4f, which waits until period 6. Shell number and period number are related, but they are not the same thing, and this is where that shows.
Reading the table backwards
So far the lesson has gone from an atomic number to a configuration. Exams go the other way: here is an element, tell me its period, group and block. Here is a configuration, tell me what it is.
There is nothing to memorise in this section. Every answer is arithmetic on the configuration you already know how to build, and the working below is six lines you could write on a paper and be marked correct for.
๐ Click any element โ Manganese
Every cell is clickable. Arrow keys move around the table once a cell has focus: left and right by atomic number, up and down by a whole period.
โจ๏ธ Or start from a configuration
Type one in and find out what it is. Any format works โ 1s2 2s2 2p6,
1sยฒ2sยฒ2pโถ, [Ne] 3s2 3p5, or the whole thing run together with
no spaces at all.
Group = ns count
One s electron is group 1, two is group 2. Helium is the exception and section 07 explains why.
Group = 12 + np count
The 12 is the ten d columns plus the two s columns to the left. So npยณ is group 15, npโต is group 17.
Group = (nโ1)d + ns
Add the d electrons and the s electrons above them. This works for chromium and copper too, because moving an electron sideways does not change the total.
Where the rules bend
Twenty elements out of 118 do not follow the filling order, and five places in the table disagree with their own logic. All twenty-five are here, and none of them are a reason to distrust the rules.
Be clear about the size of this. Ninety-eight elements out of 118 follow the diagonal rule exactly. The twenty that do not are not evidence that the rule is wrong; they are evidence that the rule is an approximation to something more careful โ and in every case the something more careful is the same idea, that a half-filled or completely filled subshell is worth going out of your way for.
Exactly two of these are on the syllabus
Chromium and copper. Learn those two, and learn the reason rather than the strings, because the reason is usually worth the second mark. The other eighteen are here so that when molybdenum turns up in a question you recognise the same bargain instead of assuming you have misremembered something.
โ๏ธ All 20 configuration exceptions
10 in this groupFive places where the table argues with itself
These are not configuration exceptions โ the configurations are fine. They are places where the cell an element is drawn in does not match what its electrons say, and every one of them is found by checking the data rather than by being listed.
How to talk about exceptions in an answer
Never write "chromium is an exception" and stop. Write what the rule predicts, write what actually happens, and name the reason: "The Aufbau order predicts [Ar] 3dโด 4sยฒ, but chromium is [Ar] 3dโต 4sยน because a half-filled 3d subshell is more stable than the extra s pairing, and 3d and 4s are close enough in energy for the swap to be worth it." Three clauses, and the third one is the one being marked.
The tug of war
This is the section that makes the next one unnecessary to memorise. There is one idea here, and the five trends in section 09 are five consequences of it.
An outer electron is being pulled on by the nucleus and pushed away by every other electron. The effective nuclear charge is what is left of that pull after the inner electrons have got in the way โ and getting in the way is called shielding.
Z is the proton count. S is the shielding, which at this level is simply the number of inner-shell electrons. Chlorine has 17 protons and 10 inner electrons, so its outermost electron feels about +7 โ not +17.
๐ชข Two walks, one picture
Step along period 3 and watch the pull climb while the shell count stays the same. Then step down group 1 and watch the pull refuse to move while the atom grows anyway.
Charge wins
Every step right adds one proton, and the electron that comes with it goes into a shell that already exists. Electrons in the same shell shield each other very badly, so almost none of that new proton is cancelled out. Zeff climbs by one at every step: sodium +1, magnesium +2, all the way to argon at +8.
Distance wins
Every step down adds a whole new shell, and every electron in the shells beneath it shields almost a full unit of charge. Caesium has fifty-two more protons than lithium and its outer electron feels the same +1. Nothing changes except how far away it is โ and that is enough to change everything.
The honest footnote
"Inner electrons shield one unit each, same-shell electrons shield none" is a simplification. Slater's rules do better โ same-shell electrons actually shield about 0.35 each, and d and f electrons shield poorly enough that the effect has a name (section 11's lanthanide contraction). But the simple version gets the direction of every trend right, and direction is what exam questions ask for.
The five trends
Five maps, and they are the same map. Once you have seen that, there are not five trends to remember โ there is one, and four things that follow from it.
Atomic radius pm
0 elements are greyed out because they have no value on this scale โ see the note below.
โ๏ธ Compare any two
Click two cells on the map above. The verdict names which is bigger and which argument applies โ the distance one for two elements in the same group, the pull one for two in the same period. Say the wrong one in an exam and you lose the mark even with the right element.
One sentence for all five
Across a period the pull rises; down a group the distance rises. Radius and metallic character follow the distance. Ionisation energy, electronegativity and electron affinity follow the pull. If you can reconstruct that one line under pressure, you can derive any of the five arrows without having learnt a single one of them.
Counting valence electrons
Everything so far has come from knowing which element you are holding. This section does the opposite: it works out a group from measurements alone, with the label covered up. It is the closest thing in the topic to doing an experiment.
Take one electron off an atom and measure what it cost: that is the first ionisation energy. Take another off the ion, and another. The numbers always rise โ every electron you remove leaves behind a more positive ion, so the next one is held more tightly. But somewhere the rise stops being gentle and becomes a cliff.
Unknown element
logarithmicEach bar is one more electron removed, left to right. Find where the cost leaps, count the bars before it, and that is how many valence electrons this element has.
How many valence electrons?
Each removal costs a little more
After the first electron leaves, the ion has one more proton than it has electrons, so everything left behind is held tighter. That accounts for the steady climb โ typically a factor of about 1.5 to 2 per step. It is not the signal.
A new shell is a different world
Once the outer shell is empty, the next electron has to come out of a complete inner shell โ much closer to the nucleus, with far less shielding in front of it. That is a factor of three to fourteen, not a factor of two, and it is unmistakable.
What the exam does with this
A table of successive ionisation energies, no element named, and a question asking for the group. Count to the jump. Two electrons before the cliff means two valence electrons means group 2; five means group 15. It is worth practising until it takes four seconds, because it is free marks and it needs no recall at all.
The families
Nothing new here โ every family's behaviour is one of the two walks from section 08 applied to a column. What is new is the vocabulary, and exams ask for the vocabulary.
๐จโ๐ฉโ๐ง Pick a family
6 membersOr click any cell on the table and it will jump to whichever family owns it.
| Element | Z | Configuration | Radius / pm | 1st IE | EN | Melts at | Ion |
|---|
The question that catches people out
Why does reactivity increase down group 1 but decrease down group 17? Because both groups are trying to reach a noble gas, and going down makes the outer shell further away. A group 1 atom wants to lose an electron, and a distant electron is easy to lose โ so caesium beats lithium. A group 17 atom wants to gain one, and a distant shell attracts a newcomer weakly โ so fluorine beats iodine. One cause, opposite consequences. Say it that way and it is one sentence instead of two facts.
Ions and the octet
Every ion in chemistry is an atom trying to look like a noble gas. Once you accept that, the charges stop being a list to learn and become something you can work out.
๐ฎ Predict the ion
Click any element. Elements with a single predictable charge are coloured; the greyed ones โ the transition metals, the metalloids, group 14 โ do not have one, and the panel says why instead of pretending.
โ ๏ธ The 4s trap
A transition metal fills 4s before 3d โ and then empties 4s first. Pick a metal and a charge and watch which electrons actually leave.
๐ Same electrons, different protons
Drawn to scale from measured ionic radii.
What happens to the size
A cation is always smaller than the atom it came from, and an anion is always larger. Both for the same reason, running in opposite directions: the number of protons never changes, so the pull per electron does.
| Atom | Radius | Ion | Radius | Why |
|---|
A note about the two scales
Atomic radii and ionic radii are measured differently โ one from the length of a bond, the other from the spacing in a crystal โ so the numbers in the table above are not strictly subtractable. What is not in doubt is the direction and the size of the change: sodium's cation is a little over half the atom on any scale you choose, and chloride is nearly twice the size of chlorine on any scale you choose.
Exam trainer
Every question here is generated the moment you ask for it and dealt from a shuffled deck, so there is no set of answers to learn. There is only the chemistry.
25 questions, one clock, a diagnosis at the end
Built to a fixed blueprint so every paper covers the same ground in the same proportions โ but with generated questions, so no two papers are alike. Free navigation: skip, come back, change your mind. Nothing is marked until you submit, and a wrong answer costs nothing, so never leave a blank.
Drills
Unlimited questions, marked and explained the instant you answer. Every one is tagged with the section that teaches it, so a wrong answer comes with a way back.
Quick check
Twenty fixed questions with a written explanation on every one. Take it once, after reading โ this is a checkpoint, not a workout.
How this differs from section 13
These twenty are the same twenty every time, and the explanations are the point of them โ each one says why the right answer is right and names the mistake behind the wrong one. Being able to remember them is fine. When you want questions that cannot be memorised, the trainer has an unlimited supply.
Flashcards
Thirty terms. Every back has the definition and, underneath it, the hook that survives a stressful morning.
Summary & cheat sheet
Everything worth having on paper the night before, on one page. Press ๐จ at the top of the screen to print it, or save it as a PDF.
๐งพ Reference table
The filling order, with capacities
Every rule in this lesson
| Topic | Rule | Note |
|---|
Before you close this
On exam day, write these three lines at the top of your paper before you read a single question: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p ยท s 2 ยท p 6 ยท d 10 ยท f 14 ยท Zeff = Z โ S: rises across, flat down. Then, for any question about an element, build the configuration first and answer the question second.