atomic radii

Trends in the radius of atoms across a period

The next main topic after this is one is to identify the trends in ionisation energies of elements. However to fully grasp the concepts involved in identifying the trends present in ionisation energies it would be helpful to quickly look at the trends in the size of atoms and ions. However you might be wondering how it is possible to measure the size of atoms with any accuracy at all, since the quantum mechanical model of the atom assumes that the electrons are present in orbitals and an orbital is a volume where there is a high probability of finding the electron and so we cannot be 100% certain of the size of these orbitals nor can we measure the position of the electron within these orbitals with 100% precision due to the uncertainty principle.

To solve this problem we assume that the atomic radius is half the distance between two atoms which are bonded to each other, it is often called the covalent radius of an atom e.g. In the diagram below there are two atoms, labelled A. The atomic radius of atom A woul be half the distance between the nuclei, so in this case the atomic radius of atom A would be 50pm (50 x 10-12m).

how to calculate atomic radius

What trends might you expect for atomic radii if you go down a group in the periodic table? Or what about as we cross a period in the periodic table?
Take the alkali metals in group I (Li, Na, K, Rb, Cs) as an example. As we go down the group an extra electron shell or principal energy level is added for each element. Li in period 2 has an electronic configuration of 1s22s, Na in period 3 has an electronic configuration of 1s22s22p631, adding the extra shell increases the atomic radii. The next element down in period 4 is potassium. Its outer shell valence electron is in a 4s sub-shell, so it will be even larger than sodium. The table below gives the covalent radii of the alkali metals.

element Li Na K Rb
atomic radius (pm) 128 166 203 290
relative sizes of atoms

Trends in atomic radius across a period

The atoms get smaller as we cross a period in the period table; this is perhaps not what you were expecting! However if you consider the electronic configurations of the elements and the increasing nuclear charge as we cross a period it is an entirely obvious conclusion. The decrease in the size of the atoms is simply because the outer shell valence electrons are all roughly at the same distance from the nucleus since they are in the same principal energy level/sub-level and the ability of electrons to shield each other from the effect of the nuclear charge is reduce by the fact that the valence electrons are all in the same shell. The amount of shielding experienced by an electron depends both on the shell and sub-shell it is in. Generally valance shell electrons are:

Since crossing period 3 the electrons are being added to the 3s and 3p sub-shells they are ineffective at shielding each other from the increasing nuclear charge. So the effective nuclear charge that each electron experiences is increasing so the atoms decrease in size as a result. This is illustrated in the diagram below:

comparison of atomic radius of elements across a period in the periodic table