Dear Dr. Phaneuf,
You are always telling us to keep electrons paired on the Lewis structures we draw. But don't electrons repel?
Confused in gen chem I
Ah, the mysterious mysteries of nature! You are right to be confused and I applaud your discerning question.
Why would electrons pair anyway, if they repel each other? Negative does repel negative, according to the electrostatic law.
Although electrons repel each other, they can “pair,” which really means they share the same energy level. Energy levels are allotted rather strictly to particles that are small, compared to things that are large. In order to share the same energy level, electrons do have to physically get closer to each other, and this does increase the repulsion they feel for each other. If this repulsion is less than the attraction that both electrons feel for the protons in a nearby atom, however, they will pair and will be more stable in doing so. Yes, two electrons that repel each other are sometimes more stable when they pair up. Nature is indeed weird--and it gets weirder.
The explanation for this pairing lies in viewing electrons as being waves rather than particles. It turns out that all particles, not just electrons, can be described as waves. So all the particles in your body are also waves. We can represent this situation more abstractly with math. (If you are frustrated in trying to picture matter as being made of waves, don’t feel bad. Most scientists don’t try to visualize this situation. While such abstractions may not be very satisfying, we know that the math, on paper, works.)
Equations called wavefunctions are used to represent particles, and since these equations predict nature’s behavior quite well, we believe they are true. A wave is something that oscillates, alternates, or, well, waves, over a period of time. You can wave you hand up and down over time, and that is a wave. If you increase the speed, you are increasing the energy of your wave. The wavefunction of a particle allows you to predict where the particle is most likely to be found around an atom, assuming it has a particular energy. If you do not have a lot of energy, you are more likely to be in bed, for example. If an electron has less energy, it is more likely to be in its “ground state,” closer to the nucleus of the atom. Higher energy electrons are more likely to be in outer regions of the atom. (They have to spend more energy remaining away from the attractive positive nucleus. Their location is like expensive real estate, and sometimes the outermost electrons get fed up, so to speak, and leave, or get shared with another atom, forming a bond.) Waves have different energies.
The smaller a particle, the more its wave energies become restricted to specific values, while other energies simply are, oddly, mathematically “forbidden.” This causes very small particles to behave in ways that seem bizarre to us. For example, when they change from one mathematically permitted energy level to another, they are first in one place and then instantaneously reappear in another place, an event called a quantum leap. The only reason this seems strange to us is because we are so massive that the energy levels accessible to us are so close in value that we perceive no gaps between them.
This constraint upon very small particles to particular energy levels also limits them to particular regions in space. The restriction of properties associated with an electron’s wave is what forces two electrons to pair up around an atom. This may not be entirely satisfactory to you, but it is the best I can do without getting into hairier quantum mechanics. Sometimes, it is unstable for a single electron to go unpaired, and any chemical possessing an unpaired electron is called a free radical.