Electronic Structure of Atoms

Representations of Orbitals

The s Orbitals

The 1s orbital is spherically symmetrical. A plot of y² versus distance (r) from the nucleus shows a dramatic reduction in probability of finding the electron very far from the nucleus:

This indicates that in the ground state the electrostatic attraction of the electron for the proton in the nucleus is such that the electron is unlikely to be found far from the nucleus.

The higher energy s orbitals are also spherically symmetrical, however, they exhibit distinct nodes in the distribution probability:

• In the higher s orbitals there exists node regions where the electron density approaches zero (2s has 1 node, 3s has 2 nodes, etc)
• The higher s orbitals (excited states) have electron density distributions which indicate that there is a higher probability of finding the electron further away from the nucleus

The most widely used representation of the Schrödinger orbits is to draw a boundary which represents 90% of the total electron density distribution. For the s orbitals this would be a sphere representation.

p Orbitals

• The p orbitals are 'dumbbell' shaped orbitals of electron density, with a node at the nucleus.
• There are three distinct p orbitals, they differ in their orientations
• There is no fixed correlation between the three orientations and the three magnetic quantum numbers (m_l)

The d and f orbitals

In the third shell and beyond there are five d orbitals, each has a different orientation in space:

Although the 3d_z2 orbital looks different, it has the same energy as the other d orbitals.

There are 7 equivalent f orbitals (for each value of n 4 or greater). They are pretty difficult to represent on a 3-d contour diagram.

Understanding orbital shapes is key to understanding the molecules formed by combining atoms

1996 Michael Blaber