In 1869 Mendeleev arranged the elements known at the time in order of atomic weight and put together a table showing that elements with similar properties appear at regular intervals. He left gaps for elements not yet found and predicted their properties. Gallium, scandium and germanium were found afterward and agreed well with his predictions.
Today's periodic table is arranged in order of atomic number, that is, the number of protons in the nucleus. As seen in the article on X-ray spectra, in 1913 Moseley showed that the atomic number can be determined from the frequency of characteristic X-rays.
The rows are called periods and the columns groups. Elements in the same group have similar properties. Lithium, sodium and potassium in group 1 are metals that react violently with water, and helium, neon and argon in group 18 are gases that hardly react at all.
The colors in the figure show which orbital, s, p, d or f, the last electron goes into when electrons are added in order of atomic number. The two columns on the left are the s block, the six on the right the p block, the ten in the middle the d block, and the fourteen set apart below the f block.
The numbers of columns, 2, 6, 10 and 14, are the numbers of electrons 2(2l + 1) that each kind of orbital can hold. Helium ends with 1s, so it is colored as s block, but its properties are close to those of the noble gases, so it is placed in group 18.
In atoms with two or more electrons, the energy depends not only on n but also on l. Each time the atomic number increases by 1, the added electron goes into the lowest-energy state that is still empty.
The order is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p. 4s comes before 3d because 4s also has probability right near the nucleus and is less shielded by the inner electrons. In potassium and calcium, 4s has a lower energy than 3d.
This order is obtained by sorting in increasing n + l and, when n + l is the same, putting the smaller n first. The figure lays out the orbitals with n down the side and l across, and joins orbitals with the same n + l by diagonal arrows. Following the arrows from the top gives the order.
This rule is called the Madelung rule. It does not hold for every element, and examples that do not follow the order are taken up in the last scene. Also, when an atom becomes an ion or forms a compound, the order of the energies of 4s and 3d can be reversed.
A period begins where electrons start to go into the s orbital of a new n, and ends where the p orbitals are filled and the element is a noble gas. The first period has only 1s, with 2 elements; the second has 2s and 2p, with 8; the third has 3s and 3p, with 8.
In the fourth period, 3d comes in between 4s and 4p, so there are 2 + 10 + 6 = 18. In the sixth period, 6s, 4f, 5d and 6p come in, giving 2 + 14 + 10 + 6 = 32. This is how the period lengths 2, 8, 8, 18, 18, 32, 32 are determined.
The third period has 8 elements rather than 18 because 3d is higher in energy than 4s and is not filled within the third period. There are 18 states with principal quantum number n = 3, but the length of a period is set not by the number of states for each n but by groups of orbitals with similar energies.
The bars in the figure show the orbitals and numbers of electrons that go into each period, colored by the kind of orbital. The 14 elements of the sixth and seventh periods in which 4f and 5f are filled form the f block, written apart below the periodic table.
The energy needed to remove one electron from an atom is called the ionization energy. The figure shows the values for atomic numbers 1 to 36: 13.6 eV for hydrogen and 24.6 eV for helium.
The values are large for the noble gases and drop sharply for the alkali metals right after them. Neon has 21.6 eV, while sodium has 5.14 eV. The 3s electron of sodium is alone in a new shell, shielded by the 10 inner electrons, and only weakly attracted to the nucleus.
Within a period, the charge of the nucleus grows with atomic number, and the ionization energy generally increases. It falls, however, from beryllium to boron (9.32 eV to 8.30 eV) and from nitrogen to oxygen (14.5 eV to 13.6 eV). In boron the first electron goes into 2p, which is higher than 2s, and in oxygen a second electron goes into one of the 2p orbitals, where the two electrons repel each other.
From scandium to copper in the fourth period, electrons go into the inner 3d, and the ionization energy stays between 6.5 eV and 7.9 eV without changing much.
Elements with smaller ionization energies more easily become positive ions, which bears on how readily they react chemically. The repeating properties of the elements in the periodic table reflect the repeating way in which electrons fill states.
When there are several orbitals with the same energy, electrons first go into separate orbitals with their spins pointing the same way. This is called Hund's rule. Electrons in separate orbitals repel each other less than two in the same orbital, and electrons with aligned spins, as seen in the article on the exclusion principle, never come to the same place.
In carbon, the two 2p electrons, and in nitrogen, the three, go into separate orbitals pointing the same way. When the fourth 2p electron comes in, in oxygen, one of the orbitals has to hold two. This is why the ionization energy falls from nitrogen to oxygen, as seen in the previous scene.
Some elements do not follow the order. Chromium would be 3\mathrm{d}^4\,4\mathrm{s}^2 by the order, but it is actually 3\mathrm{d}^5\,4\mathrm{s}^1. Copper is also 3\mathrm{d}^{10}\,4\mathrm{s}^1 rather than 3\mathrm{d}^9\,4\mathrm{s}^2. The energies of 3d and 4s are close, and a state with one electron in each of the five d orbitals with aligned spins, or with all ten filled, has a lower total energy.
The figure draws the actual electron configuration above, and below, in a lighter color, the case where electrons go in by the order.
The shape of the periodic table can be explained by the order in which electrons fill states and by the exclusion principle, which allows only one electron per state. In 1922 Bohr tried to explain the shape of the periodic table from his model of the atom, and argued that the element with atomic number 72, not yet found, was not a rare earth but an element similar to zirconium. Hafnium, found the following year, turned out as he had argued.