Atomic Radius: Definition, Formula & Example

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  • 0:00 Periodic Trends
  • 0:30 Atomic Radius
  • 2:42 How Is the Atomic…
  • 3:16 Calculating Atomic Radii
  • 4:43 Lesson Summary
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Lesson Transcript
Instructor: Marion Carroll

Marion is a 30-year veteran of industry and academia primarily in the fields of biochemistry and genomics.

In this lesson, we'll learn about the atomic radius. We'll discover methods and formulas for figuring it out and learn how it's affected by different factors.

Periodic Trends

The Periodic Table of Elements is a very useful tool. Not only does it tell you what all the elements are, it also tells you about the properties of the elements! Some of the properties have trends, called periodic trends, including atomic radius, ionization energy, and electronegativity. In this lesson, we'll learn what the atomic radius is and how to calculate it. Then we'll take a look at a couple of examples.

Atomic Radius

Simply put, the atomic radius is half of the diameter of the atom, which is a result of the number of protons, neutrons, and electrons that compose the atom. Generally, it would make sense that a large nucleus and a large number of electrons would suggest a large atomic radius. However, in reality, it is not quite so simple. As you go across a period, the atomic radius decreases. As you go down a group, the atomic radius increases. So this means that sometimes atoms with greater atomic mass are smaller in size than atoms with less atomic mass.

In order to understand how this works, let's take a step back at and look at a few fundamental concepts regarding atoms. We know that neutral atoms have the same number of protons and electrons in order to balance out the positive and negative charges. Atoms are held together by electrostatic forces, which bring negatively charged electrons closer to the nucleus by the pull of positively charged protons, much like the attraction of opposites poles of a magnet. As the valence shell becomes fuller, the negative charge becomes stronger, pulling the outer shell closer to the nucleus.

Once the outer shell is full and a new shell is added, the inner full shell blocks the outside electrons from seeing the nucleus. In other words, the full inner shell of electrons acts like a shield. This means that as you go across a period, adding electrons to the outer shell, the electro-static forces pull the electrons closer to the nucleus, which decreases the size of the atom as you move from left to right.

However, when you move to the next period, a new shell is added, which effectively increases the size of the atom. So sometimes heavier atoms have a smaller atomic radius than lighter atoms. Let's take a look at a few examples to help us understand how this works.

Here, we see Carbon (C), Nitrogen (N), Oxygen (O), Fluorine (F), Neon (NE), and Sodium (NA). As we add electrons to the outer shell, the shell is pulled closer to the nucleus. However, when a new shell is added as in the case of sodium, the size of the atom is bigger because the one electron in the outer shell does not have enough negative charge to pull the shell close to the nucleus.

Atomic Radii

How Are Atomic Radii Determined?

So, an individual atom consists of protons, neutrons, and electrons. The protons and neutrons make up the nucleus, but the electrons exist in a cloud of uncertainty as to where they are located around the nucleus. This means that the outer layer of electrons provides no definitive boundary. Like in a circle, the radius of an atom is simply half the diameter. Without knowing the boundary, a diameter of an atom is uncertain.

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