Ionization Energy (1) Definition and how its measured

Ionisation energy (1) Definition and how its measured

In this post, I’d like us to look at what we mean by Ionisation Energy and how it can be measured for a simple atom like hydrogen. 

Of course, the measurement of ionisation energy is pretty redundant these days since ionisation energies of most of the elements (those that have measurable values at least) have been determined.

So you can read off ionisation energies from tables on the Internet to your heart’s content. 

And you can spot the differences in these tables too. 

So if you are studying for a particular examination set by a particular examination board be sure to use the table of data that particular examination board provides.

What is Ionisation?

But let’s begin at the beginning and ask what is ionisation?

Neon and other noble gases will emit light if they are given enough energy.

In the example above, the energy comes from the electricity that is supplied to the different discharge tubes.

A discharge tube is a glass tube containing a gas (say neon) at a very low pressure.

The current consists of electrons flowing in the opposite direction (remember electrons are negatively charged so flow to the positive anode)

The thing is the electrical potential between anode and cathode can be increased until it is high enough for electrons from the gas atoms to lose electrons.

If an electron is removed completely from an atom it is said to be ionised.

With some gases and some metals the emission of light sometimes visible also occurs on ionisation. 

With neon gas in the discharge tube, the light emitted is red. 

Other gases give different colours.

But what’s even more interesting is to look at the emitted light using a spectroscope.

(A spectroscope is basically a sophisticated prism that splits light into its individual wavelengths and therefore colours in the visible region of the spectrum.)

If hydrogen was in the gas discharge tube here’s what you would see with the spectroscope:

The spectrum is not continuous like that of a rainbow but consists of lines of colour separated by darkness. 

You can see in the diagram a spectrum for neon’s red light similar to that for hydrogen.

These spectra are called line emission spectra.

Each set of lines is like a signature of that element. 

Each set of lines is unique to that element.

For the historians of science among you, this is how that existence of helium was established before it was found on Earth.

Its line emission spectrum was noted in the Sun’s detailed spectrum.

That’s how helium got its name, from the Greek for Sun: helios ηελιος

Explanation of line emission spectra

Why is the spectrum made up of lines of light of very precise wavelength and frequency?

The lines are evidence, neat, observable evidence, of the quantization of energy at the atomic level.

What’s that mean?

Think of a staircase in your home or college. 

Walking up or down the staircase you can only stand at certain energies thanks to the steps so that not all possible potential energies are open to you to occupy above the ground. 

Your potential energy is fixed at certain values only. 

Your energy is quantized.

Now with atoms it must be something similar.

The electron cannot occupy any old random energy.

Electrons in atoms occupy only certain allowed energies and those energies can be determined from their emission spectra using the wavelength and frequencies of the lines in the spectra.

Here’s a picture of this quantization idea that you’ll find in every A level/college text book but remember it’s not like this at all!: this is only a simple, forced representation of the reality that is the atom.  

So how do these lines in the spectrum form?

Hydrogen molecules in the discharge tube gain energy as the electricity is passed into the tube. 

As a result, the electrons in the hydrogen molecules are ‘excited’ to higher allowed energy levels, not all the same level and some electrons will become so excited that the atom will be ionized and the electron lost from the atom.

Electrons are now in energetically unstable higher energy levels, so guess what, they fall back down to lower energy levels not necessarily the ones they started from but as they do so they emit energy as light of different but specific frequencies!!

The frequency and wavelength of the light emitted will depend on the difference between the electrons’ energy levels, the lower the frequency of the line the smaller the difference between electron energy levels.

In the diagram above, the gap between levels represents the difference in energy between the lines, if you like the higher or lower the ‘steps’ in energy of the electron in the atom.

Now here is the connection between this model of the hydrogen molecule and hydrogen’s ionization energy.

Think for a minute with me, what will the largest ‘step’ in electron energy levels represent?

That’s right, its ionization energy.

All we then have to do is examine the hydrogen line emission spectrum to find the line with the highest frequency, measure it and we will be able to calculate the ionization energy of hydrogen. 

What we need then is the highest frequency line in the Lyman Series (or its lowest wavelength line) and that line is in the ultra violet region of the spectrum.

Here is the Lyman Series and its lowest wavelength line is at 912Å or 912 *10^—8 m this is also called the series convergence limit.

(Note for the historians again: Å is the old symbol for the Ångstrom unit 1Å = 10^—8 m)

We can calculate the energy of this line as follows:

Using  E= hf or E = hc/λ 

where E is the energy of the line, h is Planck’s constant, c is the speed of light and λ is the wavelength of that light.  (f is the frequency of light some times given the Greek symbol ν )

Therefore:   E =  2.998*10⁸ (m/s)*6.63*10^—34 (J.s)/  912 *10^—8 m 

                        E  =  2.179 * 10^—18 J per atom

If this value is multiplied up by Avogadro’s constant we reach a value for the hydrogen ionization energy per mole of atoms:

E  =   +1312 kJ.mol^—1  

Now your course in Chemistry might require you to be familiar with this calculation and to perform it in an examination. 

You need to satisfy yourself that you can do that.  

It is easier if you are given the highest frequency of the Lyman series, of course.

In my next post on Ionization Energy, which is likely to be shorter!! I will discuss with you how the ionization energy values of elements can be used to reveal the electronic structure of the atoms of those elements.