Look at the diagrams below, which are the same as the ones on p. 83: they represent the first three vibrational frequencies of a string. Now think about the motion of the string itself: in the first vibration, all of the string moves up and down at the same time—each point on the string moves by a different amount, but the direction moved at every point is the same. The same is not true for the second ‘energy level’ of the string—during a vibration like this, the left-hand half of the string moves upwards while the right-hand half moves downwards— the two halves of the string are out of phase with one another, and there is a change of phase at the node. The same is true of the third energy level—again, there is a change of phase at each node.

The same is true for orbitals. A nodal plane, such as that in the 2p orbitals, divides the orbital into two parts with different phases, one where the phase of the wavefunction is positive and one where it is negative. The phases are usually represented by shading—one half is shaded and the other half not. You saw this in the representation of the 2p orbital above. The phase of an orbital is arbitrary, in the sense that it doesn’t matter which half you shade. It’s also important to note that phase is nothing to do with charge: both halves of a filled 2p orbital contain electron density, so both will be negatively charged. So why is phase important? Well, in a moment we will see that, just as atoms add together to give molecules, we can add together the wavefunctions of atomic orbitals to give molecular orbitals, which tell us where electrons are, and how much energy they have, in molecules.