## Atomic Size

The first of these properties is the atomic size. You know that each atom has a nucleus inside and electrons zooming around outside the nucleus. It should seem reasonable that the size of an atom depends on how far away its outermost (valence) electrons are from the nucleus. If they are very close to the nucleus, the atom will be very small. If they are far away, the atom will be quite a bit larger. So the atomic size is determined by how much space the electrons take up.

Measuring the size of atoms is, in some ways, like measuring the size of cotton balls or automobile tires. The value you get depends on the conditions under which they are measured. A "free" cotton ball has a different size than when it is in the package. The radius of the tire is different when measured to the top of the tire than when measured to the bottom of the tire resting on the ground. Different values for the sizes of atoms are obtained depending on both the method used and the conditions in which the atoms find itself - free or bonded to other atoms. The following table gives a variety of values collected from a variety of sources.Whichever set of values you choose to use, note the trends.

Atomic Sizes (in Angstroms, which is 10-10 meter) from Various Sources

 1.58 0.3 1.2 0.98 n.a. 4.10 1.52 2.80 1.12 2.34 0.88 1.82 0.77 1.50 0.70 1.5 1.30 0.66 1.40 1.14 0.64 1.35 1.02 n.a. 1.60 4.46 1.86 3.44 1.60 3.64 1.43 2.92 1.17 2.46 1.10 1.9 2.18 1.04 1.85 1.94 0.99 1.80 1.76 n.a. 1.92 5.54 2.31 4.46 1.97 4.18 1.60 4.00 1.46 3.84 1.31 3.70 1.25 3.58 1.29 3.44 1.26 3.34 1.25 3.24 1.24 3.14 1.28 3.06 1.33 3.62 1.22 3.04 1.22 2.66 1.21 2.0 2.44 1.17 2.00 2.24 1.14 1.95 2.06 n.a. 1.97 5.96 2.44 4.90 2.15 4.54 1.80 4.32 1.57 4.16 1.41 4.02 1.36 3.90 1.3 3.78 1.33 3.66 1.34 3.58 1.38 3.50 1.44 3.42 1.49 4.00 1.62 3.44 1.4 3.06 1.41 2.2 2.84 1.37 2.20 2.64 1.33 2.15 2.48 n.a. 2.17 6.68 2.62 5.56 2.17 5.48 1.88 4.32 1.57 4.18 1.43 4.04 1.37 3.94 1.37 3.84 1.34 3.74 1.35 3.66 1.38 3.58 1.44 3.52 1.52 4.16 1.71 3.62 1.75 3.26 1.46 3.06 1.4 2.86 1.4 2.68 n.a. 2.7 2.20 2.2
Atomic diameter computed using quantum mechanical calculations, Periodic Chart of the Atoms (1979), Sargent-Welch
Atomic radii and covalent radii, "Chemical Systems," Chemical Bond Approach Project (1964), McGraw-Hill
Van der Waals radii, Handbook of Chemistry and Physics, 65th Ed. (1984), CRC Press and "Chemical Systems"

Let's make some comparisons in a family and in a period. In a family--like from hydrogen to lithium to sodium on down--the atomic size increases. As you go down a group, the size increases. As you go across a period, as from lithium to neon, notice that the size decreases. You need to remember (or memorize) those trends.

Now let's talk about why that's the case and relate it back to the various factors presented earlier. Remember that the nuclear charge and the shielding electrons combine to make the effective nuclear charge. That is a very important factor when you are comparing elements in a period. As you go across a period, the nuclear charge increases and the number of energy levels stays the same. Consequently, the number of shielding electrons stays the same and the effective nuclear charge increases. As the effective nuclear charge increases, it pulls the electrons in closer and closer to the nucleus. So as you go across a period, the increase in the nuclear charge causes a decrease in the atomic size because the electrons in the valence energy level are pulled in closer and closer.

Now let's make comparison within a family such as hydrogen down to francium (Fr). It is true that the nuclear charge is increasing, but so is the number of shielding electrons. The number of shielding electrons increases by the same amount that the nuclear charge increases. So the effective nuclear charge felt by the valence electrons stays the same. There is no increase in the effective nuclear charge but there is an increase in the number of energy levels that are being used. Consequently, the electrons in the valence energy level are further and further away from the nucleus because they are in higher energy levels. Consequently, the important factor in a vertical comparison on the periodic table is the number of energy levels that are being used because the increase in the number of shielding electrons cancels out the increase in the nuclear charge.

To summarize, as you go across a period, the increase in the nuclear charge is the most important factor because the number of energy levels stays the same. As you go down a group, the increase in shielding electrons more or less cancels out the increase in nuclear charge, leaving the increase in the number of energy levels as the most important factor. This is true not only for atomic size but for other properties as well.

If you have a sharp eye and a good memory, you may have noticed that the trend shown here as you go from lithium through neon is slightly different than what was shown in the diagram of Lothar Meyer's atomic volumes. The reason for this is something that we will be getting into a little bit later in the course. It has to do with the way that atoms attract to one another. The amount of space taken up by a collection of atoms depends not only on the amount of space taken up by the individual atoms, but also on how much they compact when they combine with one another. In Meyer's diagram, there is first a decrease in volume as you go across the table and then an increase; whereas in this diagram, there is a decrease all the way across. Meyer was measuring two factors. One was the size of the individual atoms and the second was the compressibility of the atoms when they combine with more than one of themselves. In a sense, it would be like using atomic radii for the metals and an average of covalent and van der Waals radii for the nonmetals.

### Practice with Comparing Atomic Size

For each of the following sets of atoms, decide which is larger, which is smaller, and why.

a.  Li, C, F

b.  Li, Na, K

c.  Ge, P, O

d.  C, N, Si

e.  Al, Cl, Br

### Answers for Comparing Atomic Sizes

Here are answers for the questions above.

a.  Li, C, F

All are in the same period and thus have the same number of energy levels. Therefore, the important factor is the nuclear charge. Li is the largest because it has the smallest nuclear charge and pulls the electrons toward the nucleus less than the others. F is the smallest because it has the largest nuclear charge and pulls the electrons toward the nucleus more than the others.

b.  Li, Na, K

All are in the same group and thus have the same effective nuclear charge. Therefore, the important factor is the number of energy levels. Li is the smallest because it uses the smallest number of electron energy levels. K is the largest because it uses the largest number of electron energy levels.

c.  Ge, P, O

All are in different groups and periods, therefore both factors must be taken into account. Fortunately both factors reinforce one another. Ge is the largest because it uses the largest number of energy levels and has the smallest effective nuclear charge. O is the smallest because it uses the smallest number of energy levels and has the largest effective nuclear charge.

d.  C, N, Si

Not all are in the same group and period, so, again, both factors must be taken into account. C and N tie for using the smallest number of energy levels, but N has a higher effective nuclear charge. Therefore, N is the smallest. C and Si tie for having the lowest effective nuclear charge, but Si uses more energy levels. Therefore, Si is the largest.

e.  Al, Cl, Br

Not all are in the same group and period, so, again, both factors must be taken into account. Cl is the smallest because it has higher effective nuclear charge than Al and uses fewer energy levels than Br. Which is largest is less straightforward. Al has a lower effective nuclear charge (by four), but Br uses more energy levels (by one). Because the difference in effective nuclear charge is larger, it should be the more important factor in this case, making Al the largest.

Al and Br can also be compared to one another indirectly by comparing both to Cl. Both Al and Br are larger than Cl. Al is larger than Cl because it has lower effective nuclear charge (by four). Br is larger than Cl because it uses more energy levels (by one). Because Al is larger than Cl by four "steps" and Br is larger than Cl by only one "step", Al is likely the largest of the three.