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.