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Friday, 6 February 2015

How big are atoms?

You may have heard someone mention the size of atoms, in the media or at school perhaps, and you’ll certainly have heard people talk about how small atoms are. So you may be surprised to hear that we don’t know how big atoms are - not exactly, only approximately. But why not?

There are two main problems with measuring the size of atoms - other than the fact that they’re definitely too small to measure by eye, even through a microscope:
  • Atoms don’t have defined edges
  • Atoms can change their size and shape

Atoms don’t have defined edges


We normally talk about electrons in “atomic shells”, which gives the impression of hard, discrete surfaces, like the kernel of a nut. Sometimes, instead, we say electrons travel in “orbitals”. But this conjures up an image of planetary orbitals - specific lines that electrons are restricted to, like a running track. This isn’t a good model. A better description of electrons around a nucleus is “electron clouds”. These clouds describe fuzzy areas of electron density with difficult-to-determine edges. Electron density is the same as negative charge if you assume an electron is a goo smeared out like a cloud, rather than a particle which inhabits a distinct space. This is exactly what an atom is like. We have a fancy name for it: electron density probability distributions.


example plot of electron density probability against distance from the nucleus
Electron density probability distribution. As the distance from the nucleus increases, the probability of finding electron “density” oscillates between high and low depending on the shape of the orbital and number of “nodes” (areas with no electron density). Where there are no nodes, a cross-section or "mapping" of the electron density resembles a sphere (red). For multiple nodes, electron density may be mapped as concentric circles (1 node in yellow, 2 nodes in blue). Image credit: TWDK

All this means is that, in theory, an electron can be found any distance from the nucleus, but the probability of it being found decreases exponentially as you get further away. When you get really far from the nucleus, it’s pretty much not there. To determine how big an atom is, we can draw an imaginary boundary around the atom that contains, say, 90% of the electron density. If this is our atom, our “atomic size” can differ a lot from somebody else’s, if they chose 80% or 99% of electron density as the boundary line. 90% is the usual standard atomic size.

Atoms can change their size and shape


Only isolated gas atoms are easy to estimate the size of: they have no charge and no surroundings, so they remain spherical. Most elements are not stable as isolated gas atoms, and want to form ions: atoms missing electrons or carrying extra ones. There is a simple reason for this: atoms are like buses with empty seats. People will happily empty or a fill a bus, but when it’s half-filled they all sit on a double seat by themselves (because it’s awkward to sit next to a stranger). If any number of seats in between is filled, the people sitting with strangers when others are sitting alone feel uncomfortable. Passengers in partially filled bus atoms are eager to get off or have more people get on so that nobody feels awkward. In a chemistry context, this lowers the energy of the atoms, so they are more stable.

Ions are different sizes to elements because the nuclear (positive) charge stays the same, whilst the negative charge increases or decreases. When the negative charge is smaller, the positive charge dominates and holds the electrons close, making atoms smaller. When the negative charge is bigger, the negative charge dominates and electrons move a little further away from the nucleus, making the atoms bigger. This is how electrons change the size of ions.

They can also change their shape. This happens when they bond with other ions or atoms. The radius of an atom is typically calculated by measuring the separation of the centre points of two atoms. If the atoms are the same kind, the distance is halved to give the radius. However, this doesn't give a true value because electron densities overlap. Plus, when a positive and negative ion meet, the electron density in the negative ion gets smeared towards the positive ion, becoming pear-shaped. The radius is different depending on whether you measure it towards the other ion or across (perpendicular to) it. This means we need more than one measurement to describe the size!

Electron density map of a positive and negative ion
A positive ion (left) and negative ion (right) in a bond. The electron density of the two joins and is smeared from the electron-rich negative ion towards the electron-poor positive ion, making a pear-shaped electron density map. Electron density smears like this can actually be seen using very powerful kinds of microscopes, such as an Atomic Force Microscope1. Image credit: TWDK

The identity of the ions is important too: every element has a differently charged nucleus, so they affect others more or less. It depends upon context: the same way mood depends upon where we are, what we're doing and what we did earlier.

In most models, or approximations, one atom, usually oxygen, is assumed to be fixed (even though this isn’t true) and its measured value from elsewhere is used. The remaining distance is calculated as the other atom. In a solid, each atom is surrounded on all sides by other atoms, so the electron density is assumed to be pulled in all directions equally. These atoms can pretend to be spherical.

The best way to calculate radii is still undecided, and this adds another problem: if radii are calculated different ways, it doesn't make sense to compare them.

Landé radii are calculated for solids with big negative ions and small positive ions by assuming all negative ions just touch and positive ions fit into the gaps in between them. Some question whether these assumptions are valid, and in any case the method is limited to a few compounds.

Illustrated Landé radii theory
Landé radii theory. In a solid, large negative ions (blue) just touch and a smaller positive ion (green) fits perfectly into the space between them. Image credit: TWDK

The Shannon-Prewitt radii and Pauling radii are the most widely accepted and comprehensive approximations. Pauling calculated ionic radii using the ratio of relative electronegativities (the ability of atoms or ions to attract electrons to themselves). He divided the bond distance between them according to this ratio. However, electronegativity can also be difficult to determine precisely.

Shannon-Prewitt radii are more rigorous, but more difficult to use because they depend upon many things like the number of bonds to an atom and kind of bonding. The Shannon-Prewitt model also starts by assuming the sizes of fluorine and oxygen ions measured by Pauling are correct and works out the sizes of other ions using them as a starting point.

Knowing the sizes of atoms allows us to work out the strengths of bonds and stability of chemical compounds. Estimates are good enough to make sensible guesses, but we do see some differences between experiments and theory. The more precisely we know atom sizes, the more accurate our bond strengths will be and the closer our guesses about chemical behaviour. We can also work out the structures of possible solid materials and determine which structures are impossible before we try to make them. And the better we know the sizes of ions and molecules the better able we are to design molecular filters for cleaning up pollutant solids and gases.

We still don’t know how to talk about the sizes of atoms relative to each other without making up a number for the size of one “standard” atom. We can only give a range for the sizes of atoms: biggest to smallest, or make guesses of atom identities using electron density diagrams. We’re stuck. Our perspectives of size and boundaries don’t work with the concept of atoms, and we’re still debating a compromise position.

This article was written by TWDK chemistry editor Rowena Fletcher-Wood, who is completing a PhD in environmental materials chemistry at the University of Birmingham. Rowena can be found on twitter as  @RowenaFW

References
why don't all references have links?

[1] Zhang, Jun et al. "Real-space identification of intermolecular bonding with atomic force microscopy." Science 342.6158 (2013): 611-614. DOI: 10.1126/science.1242603