Trends in the Periodic Table

The Ionization Energy

There are trends in the ionization energy both down a group and across a period. The tables below show the values for the first ionization energy of the neutral atoms, which corresponds to the removal of the least bound electron.

Ionization energies for ns¹ atoms
		I(eV)	n	Z
	H	13.60	1	1
	Li	5.39	2	3
	Na	5.14	3	11
	K	4.34	4	19

The variation down the group for the ns¹ species is a decrease in the ionization energy: this follows the reduction in penetration of the ns orbital as the group is descended, ie. as n increases. The electron in the ns orbital is therefore better screened and experiences a lower effective nuclear charge, and so becomes easier to remove. However, the ionization energies, which are equal in magnitude to the orbital energies (according to Koopman‘s theorem) do not follow the inverse square dependence on n of the hydrogenic species (as shown by the curve in the graph).

Ionization energies and Electron Affinities across the first period
		I [eV]	Electronic configuration
	Li	5.39	2s¹
	Be	9.32	2s²
	B	8.30	2s²2p_x¹
	C	11.26	2s²2p_x¹2p_y¹
	N	14.53	2s²2p_x¹2p_y¹2p_z¹
	O	13.62	2s²2p_x²2p_y¹2p_z¹
	F	17.42	2s²2p_x²2p_y²2p_z¹
	Ne	21.57	2s²2p_x²2p_y²2p_z²

The trend in ionization energy, and electron affinity, across the first period shows a general increase. This too reflects the fact that the effective nuclear charge experienced by the ionizing electron increases across the period. There are minor breaks to this rule, on going from Be to B, and from N to O.

The lower ionization energy of B than Be is due to the fact that in B the electron is being removed from the 2p orbital, which is at higher energy than the 2s orbital, and so the energy required to remove it is lower: this change in occupied orbital outweighs the increase in Z_eff on going from Be to B.

The lower ionization energy of O than N is due to the fact that in O the electron is being removed from a doubly occupied 2p_x orbital, whereas in N it is being removed from a singly occupied orbital. In the doubly occupied orbital, the electrons are close together and therefore strongly repel each other, leading to a higher energy configuration and hence a smaller energy is required to remove the electron: this change in orbital occupancy outweighs the increase in Z_eff on going from N to O.

The electron affinity is also the ionization energy of the negatively charged atom, and so we see the same trend in the electron affinity as in the ionization energy. We now see the break between C and N, rather than N and O, reflecting the fact that when N gains an electron, it must pair it in the 2p_x orbital, which results in a higher energy situation, and so a lower ionization energy of the negatively charged species, or a lower electron affinity of the neutral atom.

Atomic and Ionic Radii

If we consider the radial distribution functions of the atomic orbitals, we see that the electron density gradually falls to zero as the distance from the nucleus increases. This means that the definition of the size of an atom from the radial distribution functions is difficult, although they do show that the maxima of the functions move to larger distance as the principal quantum number of the atomic orbital increases. This means that atoms with large numbers of electrons are generally larger than atoms with only a few electrons.

The size of an ion or atom is expressed in terms of one of a range of radii.

The metallic radius is defined as half the distance between neighbouring nuclei in a metallic solid, as determined from experiment.

The covalent radius is defined as half the internuclear separation of neighbouring atoms of the same element in a molecule. This refers to nonmetallic elements.

The metallic and covalent radii are known together as the atomic radii.

The ionic radius of an element is determined from the separation of neighbouring ions in the solid, with one ion chosen as a reference. This reference ion is usually taken to be O^2-, with an ionic radius of 1.40 angstroms.

Atomic radii for Lithium to Zinc

In general, atomic radii increase down a group, and they decrease across a period. These observations reflect the magnitude of the effective nuclear charge and the electronic structure.

As a group is descended, orbitals of increasing principal quantum number become occupied, and these correspond to larger and larger orbitals, as determined by the shape of the radial distribution functions.

As a period is crossed, the electrons occupy orbitals with the same principal quantum number, but the nuclear charge, and so effective nuclear charge, increases, and so the electrons become more strongly attracted to the nucleus and the atom gets smaller as a result.

It should also be noted that the formation of a cation requires the removal of an electron, and the formation of an anion requires the addition of an electron.

On cation formation, there is now extra positive charge, so the electrons experience a greater attraction to the nucleus and the cation is smaller than the parent atom.

On anion formation, the extra electron increases the electrostatic repulsion between the electrons, and so the electron density tends to move further away from the nucleus and the anion is therefore larger than the parent atom.