The popular image of an atom as a miniature solar system, with the electrons behaving like planets orbiting a star—the nucleus—works in some situations, but we are going to have to leave it behind. The problem with this view of the atoms is that electrons can never be precisely located, and instead must be thought of as ‘smeared out’ over the space available to them. The reason for this derives from Heisenberg’s Uncertainty Principle, which you can read about in any book on quantum physics. The Uncertainty Principle tells us that we can never know exactly both the location and the momentum of any particle. If we know the energy of an electron (and with quantized energy levels we do), we know its momentum and therefore we cannot know exactly where it is. As a consequence, we have to think of electrons in atoms (and in molecules) as having a prob ability of being in a certain place at a certain time, and the sum of all these probabilities gives a smeared-out picture of the electron’s habits, a bit like blurred pictures of the vibrating strings. Because an electron is free to move around an atom in three dimensions, not just two, the allowed

‘vibrations’ it can adopt are also three dimensional and are known as orbitals, or (because we are just considering electrons in a single atom for now) atomic orbitals. The shapes of these orbitals are determined by mathematical functions known as wavefunctions. The smeared-out picture of the simple atomic orbital—the lowest energy state of an electron in a hydrogen atom—looks something like the picture on the left below. We have used shading to indicate the probability of finding an electron at any one point, but a more convenient way to represent an orbital is to draw a line (in reality a three-dimensional surface) encompassing the space where an electron spends, say, 95% of its time. This gives something like the picture on the right. This simplest possible orbital—the fundamental orbital of the H atom—is spherical, and is known as a 1s orbital. Higher energy atomic orbitals have different shapes, as you will see soon.

It’s useful to think of the atomic orbitals as a series of possible energy values for an electron, and to think of them as ‘occupied’ if there is an electron (or, as we shall see below, two electrons) at that energy level, and ‘unoccupied’ if there isn’t. In a hydrogen atom in its most stable state, there is only one electron, occupying the lowest energy 1s orbital. So, our picture of the 1s orbital makes a good picture of what an H atom looks like too. We can also represent the 1s orbital as an energy level, and the electron which occupies it as a little arrow (which we will explain in a moment).

What happens if you put more than one electron into the orbitals around an atom? Well, for reasons we can’t go into here, each orbital can hold two electrons—and only two, never any more. If you add an electron to the H atom, you get the hydride anion, H−, which has two electrons around an H nucleus (a proton). Both of the electrons occupy the same spherical 1s orbital.

We can also represent the orbital occupancy as an energy level (the horizontal line) occu-pied by two electrons (the arrows). Why do we draw the electrons as arrows? Well, electrons have the property of spin, and the two electrons allowed in each orbital have to spin in oppo site directions. The arrows are a reminder of these opposing spins.

The same is true for the helium atom: its two electrons occupy the same orbital. However, the energy of that orbital (and all of the other possible orbitals) will be different from the orbital for hydrogen because it has double the nuclear charge of hydrogen and the electrons are more strongly attracted to the nucleus. We can represent the orbital occupancy like this, with the energy level lower than the one for H because of this stronger attraction.