# Ionisation Enthalpy

When does the electron of the hydrogen have zero energy? It is impossible to know. A situation has then to be defined. It is when the electron is so far away from the nucleus of the atom that there is no attraction between them. Theoretically, this is an infinite distance away. The hydrogen atom has become ionised.

H(g) ® H^{+}(g) + e^{-}

### The first ionisation enthalpy of an atom...

¼**is defined as the energy required to remove completely the outermost electron from a gaseous atom in its ground state**.

Look at the enthalpy level diagram of the hydrogen atom on the page named The Quantum Theory. For a single hydrogen atom, the ionisation enthalpy is +2.179 x 10^{-18} J atom^{-1}. The value is usually stated in kJ mol^{-1} (+2.179 x 10^{-18} J atom^{-1} x 6.023 x 10^{23} mol^{-1} / 1000).

The ionisation enthalpy for the hydrogen atom can be calculated from the **Lyman Series** in its atomic emission spectrum. The spectral lines get closer together with increasing frequency, and the point at which they converge, called the **convergence limit**, can be taken as the frequency of the photon emitted when the electron falls from infinity to the ground state (n = 1). The equation, E = hn, is used in the calculation. If the value of the Planck constant is 6.6262 x 10^{-34} Js atom^{-1}, then the ionisation enthalpy of a single atom is calculated.

The diagram below illustrates the first ionisation enthalpy of the hydrogen atom, and the first and second ionisation enthalpies of sodium.

### A plot of the log_{10} of the successive ionisation enthalpies...

for an element provides evidence for the existence of Principal Quantum Levels, and the number of electrons that can be contained in each.

Potassium, element number 19, in chosen for this example. The first energy level (n = 1) is filled when it contains two electrons and the second (n = 2) when it holds eight. Although it is suggested here that the third energy level (n = 3) can contain a maximum of only eight electrons, it is possible for it to hold as many as 18. The maximum number of electrons that can be contained in a Principal Quantum Level is given by 2n^{2} (2 x n^{2}). When the energy levels are filling with electrons, eight go into the n = 3, then two into the n = 4, followed by another 10 added to the n = 3 level.

A more detailed study of this topic reveals the existence of sub-divisions within Principal Quantum Levels and the probability of finding electrons in volumes of space called atomic orbitals. The electronic structures of chromium and copper may not be quite as expected.