The modern atomic model

Think and discuss

Do you know of any other experiments that Schrödinger is famous for? They are not all physical experiments, they can be mental ones, too.

After studying the spectrum of many different atoms, it was found that there were more spectral lines than Bohr's atomic model could explain.

The existence of more spectral lines meant that electrons of the atom could be found in many different energy states.

By applying the principles of quantum mechanics, Austrian scientist Erwin Schrödinger (1887‑1961) concluded that each energy layer or level of an atom's shell had several sub-levels. Schrödinger also established how many levels there were in each layer and how the electrons were distributed in each one of them.

Orbitals can have different shapes and sizes. Let’s have a look.

An orbital is an area where there is a high probability (greater than 90%) of finding an electron.

Schrödinger's investigations led to the discovery of the orbitals in each layer of the atom's shell:

Layer 1: one s orbital.
Layer 2: s and p orbitals.
Layer 3: s, p and d orbitals.
Layer 4 and following layers: s, p, d and f orbitals.

To designate an orbital, the layer number and the letter indicating the type are used, for example, 2s, 5p, etc. Orbitals of the same type have the same shape, although their size gets bigger as the number of the layer increases. Therefore, orbitals 2s and 3s are both spherical, but 3s is larger.

Comparison of the orbit of an electron according to Bohr's atomic model and according to the quantum mechanical model.

The outer limit of the orbit is the area where electrons are most likely to be found. But electrons are also found in other positions.

In general, an orbital's energy depends on its layer. There are sometimes variations due to the interactions between electrons. However, it is possible to order the orbitals according to their energy.

All orbitals of the same type in the same layer have the same energy, unless the atom is in a magnetic field. Each layer represents an energy level, and each type of orbital is a sub-level.

This is the order of energy in the orbitals in the first four levels. The black arrows represent the electrons that can be found in each orbital.

The Moeller diagram is a mnemonic tool that indicates the order of the orbitals according to their energy. We can see how to use it in the following box.

The rule of diagonals, or Moeller's diagram, helps us to remember the order that we need to follow.

The diagram shows the different types of orbitals. In other words, when we write 2p, this refers to the three 2p orbitals; when we write 3d, this refers to the five 3d orbitals; and when we write 4f, this refers to the seven 4f orbitals.

The quantum mechanical model showed that the shell of an atom was organised in layers and that each layer could contain different types of orbitals: s, p, d and f.

Indicate which types of orbital are found in each of the first five layers of an atom’s shell.

First layer.
Second layer.
Third layer.
Fourth layer.
Fifth layer.

Have a look at the Moeller diagram.

Place the following types of orbital in order of increasing energy.

There is only one of some types of orbital in each layer, but there can be more than one of other types.

Complete the table by stating how many of each type of orbital can be found in the same layer of the atom’s shell.

Type of orbital	S	P	d	f
Nº. of orbitals in the same layer

Summary. The modern atomic model

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