### 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.