# Lesson Video: Atomic Orbitals Chemistry

In this video, we will learn about atomic orbitals. We will learn how to identify orbitals based on their shape, how to specify specific atomic orbitals using quantum numbers, and how to determine which orbitals in an atom electrons occupy.

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### Video Transcript

In this video, we’ll learn about atomic orbitals. We’ll learn how to identify orbitals based on their shape, how to specify specific orbitals using quantum numbers, and how to determine which orbitals in an atom electrons occupy. Historically, scientists thought the electron was a point particle which orbits the nucleus of the atom and can occupy different energy levels. This description is the Bohr model of the atom, which was proposed by the physicist Niels Bohr in 1913. But not long after in the 1920s, experimental evidence emerged that showed that electrons and other fundamental particles have wavelike properties. These discoveries led to the creation of a new branch of physics, which is called quantum mechanics.

The discovery of the wavelike properties of the electron meant that the Bohr model of the atom was incorrect. We can’t describe the electron as a particle that’s occupying some point in space and orbiting the nucleus. Instead, the electron is more like a cloud that’s spread out in space around the nucleus of the atom. Unfortunately, this electron cloud doesn’t have a well-defined position and momentum like a particle does. And some of the density of this cloud is located far away from the nucleus.

Using the mathematical framework of quantum mechanics, scientists created three-dimensional mathematical expressions to describe the shape of this electron cloud. These mathematical expressions, which are called atomic orbitals, have shapes that contain a majority of the electron density around the nucleus. So atomic orbitals tell us where an electron is most likely to be found in an atom. Looking at this cartoon, we can see that the electron density that’s described by the atomic orbital isn’t the same everywhere. We can visualize this on this graph. This graph shows us the electron density as a function of the distance from the nucleus. We can see the electron density is highest closest to the nucleus. It gradually decreases as we move further from the nucleus.

This graph shows the electron density for an atomic orbital in the first energy level. This graph shows the electron density for an atomic orbital in the second energy level. In the second energy level, the electron has two peaks of electron density with an area of no electron density in between, which is called a node. So this second energy orbital might look something like this. We have the first region of electron density, which is a sphere around the nucleus, then a spherical node where there’s no electron density with another sphere of electron density surrounding that. Looking at the graph, we’ll also notice that the electron density for the second energy orbital extends further from the nucleus than the electron density for the first energy orbital. So the second energy orbital is larger than the first energy orbital.

We see something similar for the third energy level orbital; it has three regions of electron density and two nodes. And the atomic orbital in the third energy level extends further from the nucleus than both the second and first energy level orbitals. So it’s the largest of the three. These sperically shaped orbitals are called s-type orbitals. But there are other types of orbitals that have different shapes and sizes. In chemistry, the most common orbitals we’ll encounter are the s-, p-, d-, and f-type atomic orbitals. These names stand for sharp, principal, diffuse, and fundamental. These are historical names. They were given to these orbitals based on the visual appearance of spectral lines emitted by alkali metals.

s-type orbitals are all spherically shaped. There are three p-type orbitals, each have two lobes of electron density on either side of the nucleus, giving it a dumbbell-like shape. There is a node in the plane where these two lobes meet. Each of the p orbitals is oriented around a Cartesian coordinate axis. There are five d-type orbitals. Four of them have four lobes of electron density, which gives them a shape like a four-leaf clover. Each is oriented differently in space. The fifth d-type orbital has two lobes with a doughnut-like ring around the center. There are seven f-type orbitals, but they are too complicated to draw.

The orbitals of each type collectively make up a subshell. There is one s orbital in each s subshell. The three p orbitals make up a p subshell. Within each energy level, or shell, there can be multiple subshells. In the first shell, there is only the s subshell. In the second shell, there is an s subshell and a p subshell. This pattern continues for higher energy shells. So as the energy level increases, the number of orbitals within a shell increases. We can easily refer to a subshell within a specific shell by using subshell notation. Subshell notation uses the number of the shell and the letter of the subshell. Using subshell notation, this is the 1s subshell, this is the 2s, and these three p orbitals make up the 2p subshell and so on.

We can easily refer to a specific atomic orbital by using a set of numbers called quantum numbers. The first is the principal quantum number, which is given the letter 𝑛. This quantum number tells us the energy level. For the first energy level, 𝑛 equals one. For the second, 𝑛 equals two and so on. This quantum number also tells us about the orbital size because orbital size increases with the energy level.

The next quantum number is the subsidiary quantum number, which is also called the azimuthal, orbital, or orbital angular momentum quantum number. This quantum number tells us the subshell. Each orbital type has a different value of 𝑙. For s orbitals, 𝑙 equals zero. For p orbitals, 𝑙 equals one. For d orbitals, 𝑙 equals two. And for f orbitals, 𝑙 equals 3. 𝑙 can have a value from zero to 𝑛 minus one. This corresponds to how the number of subshells increases as the energy level increases.

The next quantum number is the magnetic quantum number given the letter 𝑚 sub 𝑙. This quantum number tells us the orbital orientation. For p orbitals, this quantum number would tell us whether the orbital is oriented along the 𝑥-, 𝑦-, or 𝑧-axis. 𝑚 sub 𝑙 can have a value from negative 𝑙 to positive 𝑙. So if 𝑙 equals zero, 𝑚 sub 𝑙 can only be zero. But if 𝑙 equals one, 𝑚 sub 𝑙 can be negative one, zero, or positive one, and so on. We don’t need to worry about which values of 𝑚 sub 𝑙 correspond to which orbital orientations. It’s unfortunately not as simple as 𝑚 sub 𝑙 equals one corresponds to the p 𝑥 orbital and 𝑚 sub 𝑙 equals negative one corresponds to the p 𝑦 orbital.

All orbitals, no matter the type, hold a maximum of two electrons. Because each subshell contains a different number of orbitals, each shell can hold a different maximum number of electrons. Electrons fill orbitals in order of increasing energy according to the Aufbau principle. The order that orbitals are filled is summarized by this diagram. So hydrogen single electron will be in the lowest energy orbital, which is the 1s orbital. We can indicate that there’s one electron in the 1s orbital using a superscript. This gives us the electron configuration for hydrogen, which tells us which subshells the electrons in an atom are occupying.

Lithium has three electrons. The first two will fill the 1s sub shell. The next will go into the next highest energy orbital, which is the 2s orbital. Carbon has six electrons, which will fill the 1s and 2s orbitals. The remaining electrons will go into the next highest energy subshell, which is the 2p subshell. Neon has 10 electrons. The first four will fill the 1s and 2s subshells. The remaining six will fill the 2p subshell.

If we map which orbitals are filled on the periodic table, we’ll notice that elements in the same group tend to have similar electron configurations. For example, in the halogens, we can see that the valence electron configuration has a 4s subshell and five electrons in the p subshell. This is why elements in the same group tend to have similar chemical properties. The periodic table is often divided into blocks corresponding to which orbitals are filled there.

So far, we’ve just looked at electrons and atoms, but what about electrons and molecules? Say we have the 1s orbitals of two hydrogen atoms. If these orbitals overlap, a bond is formed. When this happens, the mathematical functions described by the atomic orbitals can add or subtract. This results in the formation of new orbitals. These new orbitals are molecular orbitals which describe where electrons are located in a molecule. And now we’ve covered everything we need to know about atomic orbitals. So before we wrap up this video, let’s work some problems.

What name is given to an atomic orbital with the quantum numbers 𝑛 equals two, 𝑙 equals one, and 𝑚 sub 𝑙 equals negative one?

Atomic orbitals are mathematical expressions that describe the location of an electron around the nucleus of an atom. Atomic orbitals come in different shapes and sizes. We can refer to a specific orbital using quantum numbers. The first is the principal quantum number which is given the letter 𝑛. This quantum number tells us the energy level the atomic orbital is in. 𝑛 equals two for the orbital in this question. So we know the orbital is in the second energy level.

The next quantum number is the subsidiary quantum number given the letter 𝑙. This quantum number tells us the orbital type or the subshell the orbital is located in. This spherically shaped orbital is an s-type orbital, which makes up the s subshell. These three orbitals are p-type orbitals, which make up the p subshell. For s-type orbitals, 𝑙 equals zero. And for p-type orbitals, 𝑙 equals one. 𝑙 equals one for the atomic orbital in this question. So we know it’s a p orbital.

The final quantum number 𝑚 sub 𝑙 is the magnetic quantum number. This quantum number tells us the orientation of the orbital. For these p orbitals, 𝑚 sub 𝑙 specifies which Cartesian coordinate axis the orbital is oriented along. However, to name an atomic orbital, we don’t need to know the orientation. We only need to specify the energy level and the orbital type using the number of the energy level and the letter of the orbital. So the name of the atomic orbital with the quantum numbers 𝑛 equals two, 𝑙 equals one, and 𝑚 sub 𝑙 equals negative one is 2p.

What is the highest occupied atomic orbital in an atom of boron?

Atomic orbitals are mathematical expressions that describe the location of an electron in an atom. In this question, we need to determine the highest occupied atomic orbital in an atom of boron. In an atom, electrons fill atomic orbitals in order of increasing energy, which is summarized by this diagram. The different subshells hold a different maximum number of electrons. The s subshell can hold a maximum of two electrons; the p subshell, a maximum of six; d, 10; and f, 14.

Atoms of boron have five electrons. The electrons will first fill the lowest-energy atomic orbital which is the 1s orbital. The 1s orbital can hold two electrons, which we indicate with a superscript. The next highest energy orbital is the 2s orbital, which can also hold two electrons. Boron’s fifth and final electron will go in the next highest energy subshell, which is the 2p subshell. From the electron configuration of boron that we just came up with, we can see the highest occupied atomic orbital is the 2p orbital.

Now it’s time to conclude this video with the most important points we learned about atomic orbitals. Atomic orbitals are three-dimensional mathematical expressions that describe the most likely location of an electron in an atom. Atomic orbitals have different shapes and sizes that we can specify using quantum numbers. In an atom, electrons fill atomic orbitals in order of increasing energy according to the Aufbau principle. Atomic orbital overlap to create bonds in molecules.