Video Transcript
Approximately how large is the radius of an atomic nucleus compared to the radius of the atom, 𝑅?
This question is asking us to compare the radius of the nucleus of an atom to the radius of an individual atom. We are also told that when making our comparison, capital 𝑅 represents the radius of the atom. Radius is a measure of length. More specifically, it is a measure of the length of a line segment from the center of a circle or sphere to its outer edge. Atoms are spherical, but to keep our diagram simple, we will draw an atom as a circle.
The nucleus of an atom is the dense core found in the center of the atom. Outside of the nucleus is the region where the electrons are found. This region is called the electron cloud. Although the edge of an atom cannot be directly measured, the radius of the atom can be visualized as the distance from the center of the nucleus of the atom to the outermost edge of the electron cloud. The nucleus of the atom contains the subatomic particles called protons and neutrons. The radius of the nucleus is the distance from the center of the nucleus to the outer edge of the nucleus.
While it’s clear to see from our diagram that the radius of the atomic nucleus is smaller than the radius of the atom, diagrams like these are quite misleading. The nucleus of an atom is considerably smaller in size than the atom. If we wanted to represent the radius of the nucleus as a fraction of the radius of the atom, then we would need to divide the radius of the atom by a pretty large number.
In fact, the radius of the nucleus of an atom is about 10,000 times smaller than the radius of an atom. Let’s say that the radius of the atom depicted in our diagram is approximately 100 picometers. If we wanted to get a rough estimate of the radius of the nucleus of this atom, we could divide 100 picometers by 10,000. The result is 0.01 picometers, which is the approximate radius of this atom.
To get some perspective, comparing the radius of an atom to the radius of the nucleus is like comparing the radius of a grapefruit to the radius of a human hair. In summary, we’ve learned that the radius of the nucleus of an atom is roughly equal to the radius of the atom divided by 10,000. Therefore, the expression that relates how large the radius of an atomic nucleus is compared to the radius of the atom, 𝑅, is 𝑅 over 10,000.
