Atomic Radius — Overview & Periodic Trend

Atomic Radius of Atoms

We know that an atom's nucleus is its center of mass. It contains protons and neutrons. But, the electrons reside in the space surrounding the nucleus. They extend as far as their electrostatic attraction to the nucleus will allow. The distance from the nucleus's center to the outermost electrons is the atomic radius. The radius' size depends on the number of electrons, protons, and orbital energy level.

Atomic Radius and the Periodic Table

The atomic radius decreases left to right across the periodic table. Why? As we move across a period, the number of core electrons is constant. We are only adding to the valence shell. Remember, valence electrons don't provide shielding. So, elements in the same period have the same shielding capacity. But, we're increasing the number of protons. The increase in protons pulls the electrons closer, lowering the atomic radii.

The atomic radius increases as we move down a group. Why? There are more electrons. The additional electrons occupy higher energy levels. How do we know the energy level? That's the principal quantum number. Higher energy levels are further from the nucleus. For example, consider lithium and sodium. Their electron configurations are $[He]2s^{1}$ and $[Ne]3s^{1}$, respectively. They each have one valence electron. And they have the same ionic charge. So, there is equal shielding in both. But, sodium's electron is in the 3s-orbital versus lithium's 2s. So, sodium has a larger atomic radius. As the energy level increase, so does the atomic radius.

(Video) Atomic Radius - Basic Introduction - Periodic Table Trends, Chemistry

by The Organic Chemistry Tutor

In this video, The Organic Chemistry Tutor explains atomic radius. He starts by discussing how we gauge an atom's radius. Unfortunately, we can't just measure it. So, we need a workaround. What can we do? We can measure the length between nuclei in a molecule. To demonstrate, he uses bromine as an example. Remember, it's one of the diatomic elements. It's always a molecule! What's the radius for a single atom? It's half the molecule's distance. Next, he demonstrates the atomic radius trend on the periodic table. He clarifies it using Bohr model diagrams to illustrate electron shielding and charge. Finally, he works on a few example problems. If you want a deeper understanding of the atomic radius trend, this video can help!

How Do Chemists Find the Atomic Radius?

The atomic radius is the distance from the nucleus' center to the valence electron shell. Generally, we can use the principle quantum number ($n$) as our basis. The larger the $n$ value, the greater our radius. But, how do chemists actually measure atomic radius? What experiments do they do? Let's find out!

Experimentally Determining Atomic Radius

How do we measure the distance between two atoms? Analytical chemists have a fancy technique called x-ray crystallography. Let's explore how it works!

First, what is a crystal? A crystal is an ordered, repeating structure. Many different compounds create them. All ionic bonds are crystals. Why? It's because the atoms bond in repeated patterns. One set is a unit cell. Repeated unit cells form a crystal lattice. But, covalent compounds can also generate crystals. How? An identical molecular geometry repeats itself. One example is diamond. In it, carbon-carbon bonds form repeating tetrahedrons. Metals and metallic bonds are also considered crystals.

Now, what about x-rays? They are a variety of electromagnetic radiation. But, they have minuscule wavelengths (0.1 -10.0 nanometers). Their wavelength is about the same as the distance between bonded atoms. So, what happens when we hit a crystal with x-rays? The x-ray bounces off the atoms' electrons. That's diffraction! Then, a sensor detects the diffracted x-rays. A computer converts the x-ray's deflection angle to a position. So, we know the atoms' locations. At that point, it's easy to find the distance between them. That would be the bond length. Halving the bond length gives us the atomic radius. Remember, chemists are super creative. So, we call the radius in ionic compounds the ionic radius. Covalent compounds have covalent radii. Metals have metallic radii.

What about atoms that don't bond? For example, the noble gases all have complete octets. So, they shouldn't form bonds. But they can still create crystals! How? They interact through Van der Waal's forces. Electrons are always moving around the atom. Sometimes, more electrons are on one side than the other. What's the result? A dipole! One side has a slight positive charge. The other side is partially negative. So, atoms can experience electrostatic attraction! At low temperatures, atoms have less kinetic energy. They don't move as much. So, Van der Waal's forces are strong enough to hold two atoms together. What is the result? A crystal structure. The fancy term is molecular crystal. Using x-ray diffraction on a molecular crystal gives us the Van der Waal's radius.

Computational Chemistry and Theoretical Methods

Let's say you didn't want to measure an atom's radius. Could you calculate it? At first, it may not seem challenging. Just gauge the distance between the center of the nucleus and the valence electrons. But, there's a problem! We have to remember our studies of quantum mechanics. Where are the valence electrons? We don't know. Remember, atomic orbitals give us a probability. Consider our electron cloud diagram. Our electron could be at any one of those places. So, computational chemists use theoretical models based on atomic orbitals. It's not an exact measurement. Instead, it's a calculation that defines the most probable radius. But, the math is complex. So, you need a computer to do it.