Ionization Energy (2) The Electron Configuration of Atoms

Here’s my second blog on Ionization energy.

We are going to look at how ionization energy values lead to information about atomic electron energy levels, you know, that stuff you learned in school chemistry where the shell structure of an atom is 2)8)1 for sodium and 2)8)7 for chlorine etc….. yes??

But a couple of clarifications first. 

We need a formal standardized definition for Ionization energy.

This is it:

The first ionization energy of an element is the energy required to remove one mole of electrons from one mole of atoms of the element in the gaseous state to form one mole of gaseous ions. 

I’ve highlighted the key points in the definition from exam mark schemes that will get you marks.

And there are no short cuts for you guys who are learning chemistry for an advanced examination: you just have to memorize this definition. Yo!!

It also states that it is the definition of the first ionization energy.

What’s that mean?

Well, it refers to the removal of the first mole of electrons from a mole of the atoms.

Here’s the equation that goes with the definition:

M(g)  =   M+(g)   +    e^—

which for hydrogen would be:

H(g)  =  H+(g)   +    e^—     E_m1   =   +1312 kJ.mol^—1 

Note the symbol here for first (_m1) ionization energy.

And I guess you can see why it and all ionization energies are  endothermic values? Yes??

So the  ionization energy values refer to the removal of successive electrons from the atom and therefore this would be the equation for the fifth ionization energy of sodium:

Na⁴⁺ (g)     =     Na⁵⁺ (g)    +   e^—

And don’t you forget the state symbols every time!!

The other thing I want to do before we go any further into this area, is to go back to the diagram of electron energy transitions and explain why so many examples found in the Internet use units of eV, electron volts for ionization energy not kJ mol^—1

If you are working in the American educational system then I am guessing that you will be used to using eV, electron volts rather than kJmol^-1 units for ionization energies, yes??

Here’s what you can get from Wikipedia on the eV:

The electronvolt (symbol eV; also written electron volt) is a unit of energy equal to approximately 160 zeptojoules (symbol zJ) or 1.6×10^—19 joules (symbol J). By definition, it is the amount of energy gained (or lost) by the charge of a single electron moved across an electric potential difference of one volt. Thus it is 1 volt (1 joule per coulomb, 1 J/C) multiplied by the elementary charge (e, or 1.60×10⁻¹⁹ C). Therefore, one electron volt is equal to 1.60×10⁻¹⁹ J.

So when those electron energy level diagrams show the ionization energy of hydrogen to be 13.6eV then we can convert the eV value to Joules if we multiply it by 1.6*10^—19 and doing that gives us 21.76 *10^—19 J which if you recall was the ionization energy value per atom we calculated in the previous post. 

Simples!!!

Right let’s look now at what can we learn from the first ionization energy values of an element.

Here is a plot of the log(10) values of sodium’s successive ionization energy values for each successive electron removed (n):

Of course, you could do this sort of plot yourself on a simple spread sheet.

Can you see a pattern to these values?

And of course that’s the point here it’s not the points themselves but the dislocations.

The dislocations separate the electron energy levels or what were called shells in school chemistry. 

They are between the 1st  and 2nd electron removed and between the 9th and 10th electron removed.  

So we can see two major dislocations that give us three discrete electron energy levels (remember the ‘steps’ in the first blog?) in the atoms of sodium. 

This set of three corresponds to the three shells you would have learned about in school chemistry.

And there is the 2)8)1 pattern, electrons in three distinct groups for sodium.

But its not quite like that is it, why?

The ionization energies keep increasing in fact that's the general trend in these values. 

And these successive ionization energies increase because the charge on the ion from which the electron is being removed is increasing each time. 

So the last of 11 electrons removed comes from a sodium particle with a charge of 10+!

That's going to have a very large ionisation energy, isn't it!!

The other reason for the general increase in successive ionization energies is that the ion is shrinking in size after each electron is lost so the force on the next electron removed is greater even if the overall charge were not to increase. 

The question is what does this pattern suggest about the arrangement of electrons in atoms?

We can say first that there are just 2 electrons in the lowest electron energy level.

This energy level or shell is given a principle quantum number of n=1

The second level or shell contains a maximum of eight electrons. 

It is given principle quantum number n=2.

And as more atoms of elements are examined a pattern emerges in which the total number of electrons per energy level is related to the principle quantum number.

Principle quantum number (n)	Number of electrons per shell
1	2
2	8
3	18
4	32

The relationship is this: 

n (principle quantum number) = 2n²  (electrons per shell)

There are other representations of this pattern that you will find sometimes baffling in the standard text books.

The electrons in boxes is fairly helpful and common. 

So sodium’s pattern looks like this:

So why the arrows and why are they pointing in opposite directions?

And why is the second level split into two groups of electrons?

Well, all that is for the next post when I’m going to be discussing sub—shells and Hund’s Rule and other complexities that arise when atoms begin to increase in size and the principle quantum levels start to overlap one another.  

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.