IB syllabus > atomic theory > 12.2 

These notes were written for the old IB syllabus (2009). The new IB syllabus for first examinations 2016 can be accessed by clicking the link below.

IB syllabus for first examinations 2016

12.2 - Electronic structure of atoms

12.2.1 - Evidence for the existence of energy levels and sub-levels.

Scientists deal with a microscopic world that can never be seen. So how do they "know" the structure of an atom?

It is rather like a birthday present that arrives well wrapped. The recipient may try to guess the contents of the package without actually opening it. Many people shake the box, listen to the movement of the contents, try to gauge the weight and how the contents move around in the box.

What they are doing is putting energy into the box and by sensing the response from the box they hypothesise (guess) what the contents are.

Its the same procedure with scientists and the microscopic world.

Energy is given to the particles (atoms, molecules or ions) and the response from the unseen world is detected. Hypotheses are formulated which are then tested by all available means. If the experimental evidence seems to fit the hypothesis then a theory is proposed which in time comes to be accepted as the "truth".

The three pieces of evidence are as follows:


Different types of spectra have already been covered in section 2.2 summarised as:

Line emissions arise from energy being emitted by the atom as a result of electrons in high energy levels returning to their ground states. The electrons must emit the difference in energy and this is seen as light (electromagnetic radiation) of a specific wavelength. They first arrive at the higher level by absorbing energy in the form of either heat or electricity.



E = energy of the emission

h = Plancks constant (6.02 x 10-34)

n = frequency of the radiation (the frequency is related to the wavelength by c = ln, c is the speed of light and l is the wavelength)


Hydrogen spectrum transitions
giving series of lines in the visible range
due to transitions --> n=2:(Balmer series)

Ionisation energies

The ionisation energy of the elements can be determined by several means. These are beyond the scope of the IB syllabus. Students must understand the definitions of 1st and successive ionisation energies and also the factors that affect them, specifically electrostatic forces.

The first ionisation energy

The first ionisation energy is defined as the energy required to remove one mole of electrons from one mole of gaseous atoms to provide one mole of gaseous single charged ions.

Na(g) --> Na+(g) + 1e

Subsequent ionisation energies are defined in a similar way only by removing electrons from already charged ions.

The second ionisation energy

Na+(g) --> Na2+(g) + 1e

Successive electrons can be stripped from an atom until there is only the nucleus left. If the energy required to achieve this for each ionisation is plotted on a graph (with a log scale) against the ionisation number, the 'jumps' in the required energy clearly show the main and sub energy levels.

In this example it may be seen that removal of the first three electrons requires (relatively) less energy than removal of the next (eight) electrons - there is a distinct inflexion (change of direction) in the otherwise fairly linear graph. Consequently the element concerned must be in group III.

Many exam questions focus on the ability of a student to recognise this inflexion from purely numerical data and then ask for details of its group in the periodic table.


In the following table identify the groups to which the elements X, Y and Z belong.

Ionization Energies (kJ/mol)
1st IE
2nd IE
3rd IE
4th IE

It may be seen that the inflection (relatively bigger jump) for element X occurs between 1st and 2nd ionisation energies. It is therefore in group 1. Similarly the inflection for Y occurs between the 2nd and 3rd ionisation energies and so it is in group 2.

1st ionisation energies of successive elements

This graph shows how the first ionisation energy varies moving from element to element in the periodic table. The outermost electron is being removed in each case and so the amount of energy needed to remove it is a function of the force holding the electron in position around the atom.

This force is dependent on two main factors and is fine tuned by a third factor.

  • The charge on the nucleus
  • The distance of the outer electron from the nucleus
  • Electrons between the outer electron and the nucleus (fine tuning)

As the charge on the nucleus increases so the energy required to remove the electron increases.

As the distance between the outermost electron and the nucleus increases so the energy required to remove it decreases.

The graph is probably best understood by referring to specific examples.

Comparing the I.E. of H and He

If we compare the energy required to remove the outermost electron of hydrogen (element number 1) and helium element number 2) we see that approximately twice the energy is needed for helium. As the nuclear charge of helium is twice that of hydrogen we can conclude that the electron is roughly the same distance from the nucleus in both cases.

Comparing the I.E. of He and Li

Moving from helium to lithum, the nuclear charge increases from 2+ to 3+ . We could expect then that the energy required to remove the lithium electron would be greater that that of helium by a factor of approximately x1.5 (1.5 times greater). However, we find that the energy required to remove the lithium electrron is far less than that (in fact it is far less than the ionisation energy of both H and He). We must conclude that the second factor is coming into play - the distance from the nucleus. The outermost electron of the lithium atom is much further away from the nucleus and is therefore much easier to remove. This is consistent with our view of moving from energy shell 1 to energy shell 2.

Comparing the I.E. of Li and Be

There is an increase in ionisation energy moving from lithium to beryllium consistent with the increasing nuclear charge changing from 3+ to 4+ although perhaps attenuated (modified) by the presence of other electrons nearby.

Comparing the I.E. of Be and B

Moving from Beryllium to boron the nuclear charge increases from 4+ to 5+ suggesting that more energy should be needed BUT there is a decrease in the 1st ionisation energy. This can only be explained by the existence of a sub-shell that is slightly further from the nucleus than the region of space in which the Be electron is found.

This is our first evidence for the existence of sub-shells. The is called the "p" sub-shell and consists of three orbitals (px py and pz) each shaped like a figure of eight, and arranged along the axes of a three dimensional graph.

In general moving across a period we would expect a gradual increase in 1st ionisation energy due to the gradual increase in nuclear charge. When this does not happen in practice we must usually assume that the distance factor is more important. However, there is another anomalous change moving from nitrogen to oxygen. The graph descends instead of the expected increase. This can only be explained by considereing that the outermost electron is in a p orbital which it shares with another electron. This creates inter-electron repulsion reducing the overall force holding the electron to the nucleus and decreasing the energy needed to remove one of them. (this is also apparent in the 1st ionisation energies of Li and Be. Although the energy needed to remove the 1st electron from Be is greater than for Li, it is less than the expected increase as calculated by considering only the nuclear charge increase from Li to Be)


12.2.2 - State how orbitals are labelled. Limit this to n < 5

Having identified the evidence for energy shells and sub-shells as well as the existence of orbitals they must be named to avoid confusion.

The main energy levels are represented by the letter "n".

The Energy Levels are numbered n=1 (also called the ground state) n=2, n=3, n=4, etc all the way to n=infinity (the levels converge to the maximum possible energy that an electron can have before it escapes from the atom. After this point the nucleus no longer can hold the electron and it is said to be at infinite distance)

Atomic orbitals are the regions of space in which there is a 99% probability of finding a particular electron.

In the first energy level there is only one orbital - designated the letter "s"

In the second energy level there are s and p sub-shells. The "s" sub-shell contains only one s orbital and the p sub-shell comprises three p orbitals

n = ( level 1: s) (level 2: s and p) (level 3: s, p and d) (4: s, p, d and f)

Historically the letters used to designate the sub-shells come from words used to describe the lines seen on the spectra studied at the time. s stands for the term "sharp" , "p" for "principal, "d" for "diffuse" and "f" for "fundamental" - IB students do not need to know this.


12.2.3 - State the relative energies of s, p, d and f orbitals

The relative energies of the subshells are: s < p < d < f (within a given energy level)

It should be remembered that in spite of this order the 4s electrons fill up before the 3d electrons when applying the Aufbau principle, and that there are anomalies in the configurations of chromium, [Ar] 4s1 3d5 and copper, [Ar] 4s1 3d10 due to the extra stability of half full and full sets of "d" orbitals respectively.



12.2.4 - State the number of orbitals at each energy level

This is usually shown in graphical form. Click on the link to see the Aufbau principle in practice.

The number of orbitals at each level : s=1, p=3, d=5, f=7

Level 1: has only one s orbital

Level 2: has one s and three p orbitals

Level 3: has one s, three p and five d orbitals

Level 4: has one s, three p, five d and seven f orbitals



12.2.5 - Draw the shape of an s orbital and the shapes of the px, py and pz orbitals

Shapes of orbitals:

s- orbitals
p- orbitals
1s orbital
2s orbital
3s orbital
Px orbital
Py orbital
Pz orbital


12.2.6 - State the Aufbau principle. Reference should be made to Hund's rule

The Aufbau principle just means the way the electrons fit into the atomic orbitals in order of ascending energy. The first electron goes into the lowest enrgy orbital available (the 1s orbital) the next electron pairs up with it in the same orbital and the third electron (that of lithium) fits into the next orbital up, the 2s orbital.

The rules for filling up the orbitals are as follows:

1. Electrons always enter the orbital of lowest energy

2. If there are two or more degenerate orbitals (meaning that they have the same energy) then the electrons will singly occupy the degenerate orbitals until the orbitals are all singly occupied, after which they will pair up one at a time. This is known as Hunds rule

3. There cannot be more than two electrons in any one orbital.

Still having problems with this topic?

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Useful links

The hydrogen spectrum

Interactive Hydrogen spectrum applet