1.11. Putting electrons in boxes

At this point think back to what you know about an s sub-shell.

Two such electrons with opposed spins are said to be paired and are conveniently represented in a so called box diagram.

Given a full atomic orbital can contain up to two electrons with opposing spins. This may be simply represented by writing one electron as an upward-pointing half-headed arrow, and the other as a downward pointing half-headed arrow.

And each orbital is drawn as a box into which these half-headed arrows are drawn.

For example, the helium atom has the electronic configuration 1s². As the 1s sub-shell contains just one orbital, this can be depicted by a single box containing the two electrons (Figure 10).

Figure 10 Electron in box depiction of a helium atom

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A box diagram of a helium atom, showing one electron as an upward-pointing half-headed arrow, and the other as a downward pointing half-headed arrow. '1s' is written beneath the diagram.

Figure 10 Electron in box depiction of a helium atom

Now consider the box diagram for nitrogen.

The 1s and 2s sub-shells contain one orbital each, and the 2p sub-shell contains three. The box diagram that must be filled therefore takes the form shown in Figure 11:

Figure 11 Box depiction of atomic orbitals

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Image showing a series of (blank) box diagrams in three groups. One box stands alone and ‘1s’ is written beneath it, then another standalone box says '2s' beneath it, then three boxes are grouped together, with '2p' written beneath.

Figure 11 Box depiction of atomic orbitals

So how do the three 2p electrons fill the 2p sub-shell?

There are several possibilities, but the one you want is the ground-state arrangement, the state of lowest energy.

There is a simple rule, called Hund's rule, which tells you that within any sub-shell, there will be the maximum number of electrons with spins of the same sense.

Because electrons in the same box must have opposed spins, they must, as far as possible, go into different boxes with spins of the same sense, or, as it is usually termed, with parallel spins. In this case there are three 2p electrons and three boxes, so each box can take one electron with the same spin, and this is the preferred arrangement according to Hund's rule. The final result for the nitrogen atom is therefore (Figure 12):

Figure 12 Electron in box depiction of a nitrogen atom

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This diagram shows 5 boxes in a row, from left to right, the first is labelled 1s, the second is labelled 2s, and the three on the right hand side are positioned close together and collectively labelled 2p. Single headed arrows are arranged in each box. The boxes labelled 1s and 2s contain two arrows oriented in opposite directions. The 2p boxes each contain one arrow oriented in the same direction.

Figure 12 Electron in box depiction of a nitrogen atom

The oxygen atom has atomic number 8. Draw a box diagram for oxygen.

Answer

As there are four 2p electrons and only three 2p boxes, the fourth 2p electron cannot have a spin parallel to the other three. It must go into a box that is already occupied by one electron with opposite spin (Figure 13):

Figure 13 Electron in box depiction of an oxygen atom

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This diagram shows 5 boxes in a row, from left to right, the first is labelled 1s, the second is labelled 2s, and the three on the right hand side are positioned close together and collectively labelled 2p. Single headed arrows are arranged in each box. The boxes labelled 1s and 2s contain two arrows oriented in opposite directions. The first 2p box (i.e. the 3rd box in the row of 5) contains two arrows oriented in opposite directions. The other two 2p boxes each contain one arrow oriented in the same direction.

Figure 13 Electron in box depiction of an oxygen atom