Main content

## Chemistry library

### Unit 7: Lesson 3

Quantum numbers and orbitals# Quantum numbers

An orbital is a region around an atom's nucleus where electrons are likely to be found. Different types of orbitals (s, p, d, f) have different shapes and can hold different numbers of electrons. Learn how quantum numbers are used to describe the orbitals, and compare Bohr model orbits with the quantum mechanical model of atom. Created by Jay.

## Want to join the conversation?

- I m confused with the word orbital! Is orbital and sub-shell or sub-energy level the same thing? If not, then what is the difference ?(31 votes)
- An orbital is a "3D cloud" of possible positions of an electron (quantum mechanics states that the position is not certain). The quantum model is different from the Bohr model where the position is certain and the electron is in an orbit. There are many different individual
**shells**of these orbital "clouds", which is described by the quantum number n. n describes the electron's distance from the nucleus, which also gives the energy of the electron. A**subshell**is contained within a shell. It's possible that there is more than one subshell per shell. The shape of a**subshell**is described by the quantum number ℓ. ℓ can be any positive integer from 0 to n-1. So, there is the possibility of many subshells of many shapes. Since**subshells**of a shell share the space of that shell, they must have the same energy levels.

For Example:

There is an electron with n=4. Therefore there is individual**shells**of electrons, each with a larger energy level than the previous. Since ℓ can be from any positive integer 0 all the way to n-1, and if n=4, then ℓ can be 0, 1, 2, and 3. So, there are 4**subshells**of 4 different shapes within the n=4 shell. The 4 subshells, though they have different shape (and orientation through the other quantum numbers), are contained within the shell, therefore they all have the same level of energy.(44 votes)

- Why even give a spin quantum number if the electron isn't really spinning on an axis in reality?(39 votes)
- I think it's to account for the fact that in each orbital the electrons are "spinning" in opposite directions. Basically while they move around in the orbital they also have angular momentum. So the 1/2 and -1/2 is to account for that. We just call it "spin" to make it easier to understand the concept of what the 1/2 and -1/2 describe.(8 votes)

- Why is the spin quantum number +1/2 up or -1/2 down ? Where does the 1/2 come from ?(10 votes)
- That value comes from some very difficult math involved in quantum physics. You need to have mastered calculus at least through differential equations and vector calculus even to be able to read the equations properly. So, at this level of study we typically just tell the students the results of all the math, but skip the actual computations.(22 votes)

- What is the shape of a d- and f- orbital?(13 votes)
- They're a little more complex but here's an example of a d orbital (from wikipedia):

http://upload.wikimedia.org/wikipedia/commons/5/58/D_orbitals.png

and here is an example of an f orbital (also from wikipedia):

http://upload.wikimedia.org/wikipedia/commons/b/bb/F-orbitals.png(10 votes)

- In this video, we talk about n as the number of shell but the hydrogen atom has only one shell of type s so why the electron in this atom can "jump" down (up) to lower energy levels to emit light with different frequencies when there is only the case where n = 1 because otherwise we would have l > 0 so we would also have p orbitals, right?. I'm confused :D . Can someone help me understand?(7 votes)
- The shells still exist (or, more accurately, are available) even if there are no electrons occupying them. Thus, an electron can absorb just the right amount of energy and change from its usual state to an excited state.

By analogy, suppose that someone usually sings in the baritone range. Well, that person might be able to sing in a falsetto and reach the alto range. When they do that, their voice has jumped from its normal state to a higher state. Something no completely unlike that happens with electrons. They have their ordinary states, but if they absorb just the right amount of energy they can jump from their normal state to an excited state.

And, yes, the shell n=1 has only an s subshell, so a 1s electron must move into a different shell in order to achieve an excited state. Similarly shell n=2 has only s and p subshells, so a 2p electron would have to move into a greater shell in order to achieve an excited stated. However a 2s electron could jump to a 2p orbital (if they weren't all full) and achieve an excited state that way.

Thus, when we say that an atom does not have this or that shell, what we mean is that in its ground state that shell is not occupied.(17 votes)

- according to the quantum mechanics how many energy levels can be found ?(8 votes)
- In theory, there are an infinite number of energy levels. Practically, there are 7 energy levels(k,l,m,n,o,p,q -- we also assign these numbers 1-7) and there are 4 sublevels (s,p,d,f)(12 votes)

- What's the reason of introducing four quantum numbers only? And why is ( l ) always equal to zero when ( n ) is equal to 2?

And why are the orbitals named as s, p, d and f? How do we know how many electrons an orbital contains?(4 votes)- A quantum number describes a specific aspect of an electron. Just like we have four ways of defining the location of a building (country, state, city, and street address), we have four ways of defining the properties of an electron, or four quantum numbers.

The minimum value of "l" is zero because no atom can exist without a subshell. If l = 0, we know that the shape of the s subshell is spherical. And we also know that every atom**must**have at least one s subshell. So, considering any atom, "l" must start from zero and go on till n-1

The s, p, d, and f stand for sharp, principal, diffuse and fundamental, respectively.

The letters and words refer to the visual impression left by the fine structure of the spectral lines which occurs due to the first relativistic corrections, especially the spin-orbital interaction.

The maximum number of electrons an orbital can hold is two. So, the capacity of each subshell is:

s-subshell : maximum of 2 electrons (as it contains only 1 orbital)

p-subshell : maximum of 6 electrons (as it contains 3 orbitals)

d-subshell : maximum of 10 electrons (as it contains 5 orbitals)

f-subshell : maximum of 14 electrons (as it contains 7 orbitals)(8 votes)

- But in my NCERT textbook, it says that An electron

spins around its own axis, much in a similar

way as the earth spins around its own axis while

revolving around the sun. I'm confused.(2 votes)- They’re teaching you a simplification in a way that you can relate it to something you know. But electrons do not really spin around an axis.(9 votes)

- What does the S,P,D and F in the names of the orbitals stand for?(4 votes)
- The orbital shells are given the names s,p,d,f base on the Spectroscopic transitions involving energy levels with different angular momentum (L) values with different groups of lines in the line spectra of the alkali metals.

The s, p, d, and f stand for "sharp," "principal," "diffuse," and "fundamental," respectively.(4 votes)

- What is the difference between an orbit and an orbital? Did Bohr give the theory of orbital or does it come under quantum mechanics? Please do guide.(2 votes)
- The Bohr model of the atom did not have orbitals only orbits. It was quantum mechanics that gave us the description of orbitals.(5 votes)

## Video transcript

- [Voiceover] In the Bohr
model of the hydrogen atom, the one electron of hydrogen is in orbit around the nucleus at
a certain distance, r. So in the Bohr model, the electron is in orbit. In the quantum mechanics
version of the hydrogen atom, we don't know exactly
where the electron is, but we can say with high probability that the electron is in an orbital. An orbital is the region of space where the electron is
most likely to be found. For hydrogen, imagine a sphere, a three-dimensional volume, a sphere, around the nucleus. Somewhere in that region of space, somewhere in that
sphere, we're most likely to find the one electron of hydrogen. So we have these two competing visions. The Bohr model is classical mechanics. The electron orbits the nucleus like the planets around the sun, but quantum mechanics says we don't know exactly where that electron is. The Bohr model turns out to be incorrect, and quantum mechanics has
proven to be the best way to explain electrons in orbitals. We can describe those
electrons in orbitals using the four quantum numbers. Let's look at the first
quantum number here. This is called the
principal quantum number. The principal quantum
number is symbolized by n. n is a positive integer,
so n could be equal to one, two, three, and so on. It indicates the main energy level occupied by the electron. This tells us the main energy level. You might hear this referred
to as a shell sometimes, so we could say what kind
of shell the electron is in. As n increases, the average distance of the electron from
the nucleus increases, and therefore so does the energy. For example, if this was
our nucleus right here, and let's talk about n is equal to one. For n is equal to one,
let's say the average distance from the nucleus
is right about here. Let's compare that with n is equal to two. n is equal to two means
a higher energy level, so on average, the electron is further away from the nucleus, and has a higher energy
associated with it. That's the idea of the
principal quantum number. You're thinking about
energy levels or shells, and you're also thinking about average distance from the nucleus. All right, our second quantum number is called the angular
momentum quantum number. The angular momentum quantum number is symbolized by l. l indicates the shape of the orbital. This will tell us the
shape of the orbital. Values for l are dependent on n, so the values for l go from zero all the way up to n minus one, so it could be zero, one, two, or however values there
are up to n minus one. For example, let's talk about the first main energy level, or the first shell. n is equal to one. There's only one possible
value you could get for the angular momentum
quantum number, l. n minus one is equal to zero, so that's the only possible value, the only allowed value of l. When l is equal to zero,
we call this an s orbital. This is referring to an s orbital. The shape of an s orbital is a sphere. We've already talked about
that with the hydrogen atom. Just imagine this as being a sphere, so a three-dimensional volume here. The angular momentum quantum number, l, since l is equal to zero, that
corresponds to an s orbital, so we know that we're talking
about an s orbital here which is shaped like a sphere. So the electron is most likely to be found somewhere in that sphere. Let's do the next shell. n is equal to two. If n is equal to two, what
are the allowed values for l? l goes zero, one, and so on all the way up to n minus one. l is equal to zero. Then n minus one would be equal to one. So we have two possible values for l. l could be equal to zero, and l could be equal to one. Notice that the number
of allowed values for l is equal to n. So for example, if n is equal to one, we have one allowed value. If n is equal to two, we
have two allowed values. We've already talked about
what l is equal to zero, what that means. l is equal to zero means an s orbital, shaped like a sphere. Now, in the second main energy level, or the second shell, we
have another value for l. l is equal to one. When l is equal to one, we're
talking about a p orbital. l is equal to one means a p orbital. The shape of a p orbital
is a little bit strange, so I'll attempt to sketch it in here. You might hear several
different terms for this. Imagine this is a volume. This is a three-dimensional
region in here. You could call these
dumbbell shaped or bow-tie, whatever makes the most sense to you. This is the orbital, this
is the region of space where the electron is most likely to be found if it's found
in a p orbital here. Sometimes you'll hear
these called sub-shells. If n is equal to two,
if we call this a shell, then we would call these sub-shells. These are sub-shells here. Again, we're talking about orbitals. l is equal to zero is an s orbital. l is equal to one is a p orbital. Let's look at the next quantum number. Let's get some more space down here. This is the magnetic quantum number, symbolized my m sub l here. m sub l indicates the orientation of an orbital around the nucleus. This tells us the
orientation of that orbital. The values for ml depend on l. ml is equal to any integral value that goes from negative l to positive l. That sounds a little bit confusing. Let's go ahead and do the
example of l is equal to zero. l is equal to zero up here. Let's go ahead and write that down here. If l is equal to zero, what are the allowed values for ml? There's only one, right? There's only one. The only possible value we
could have here is zero. When l is equal to zero ... Let me use a different color here. If l is equal to zero, we know we're talking about an s orbital. When l is equal to zero,
we're talking about an s orbital, which is
shaped like a sphere. If you think about that, we have only one allowed value for the
magnetic quantum number. That tells us the orientation, so there's only one orientation for that orbital around the nucleus. And that makes sense, because a sphere has only one possible orientation. If you think about this
as being an xyz axis, (clears throat) excuse me, and if this is a sphere, there's only one way to
orient that sphere in space. So that's the idea of the
magnetic quantum number. Let's do the same thing
for l is equal to one. Let's look at that now. If we're considering l is equal to one ... Let me use a different color here. l is equal to one. Let's write that down here. If l is equal to one, what are the allowed values for the magnetic quantum number? ml is equal to -- This goes from negative l to positive l, so any integral value from
negative l to positive l. Negative l would be negative one, so let's go ahead and write this in here. We have negative one,
zero, and positive one. So we have three possible values. When l is equal to one, we
have three possible values for the magnetic quantum number, one, two, and three. The magnetic quantum number
tells us the orientations, the possible orientations of the orbital or orbitals around the nucleus here. So we have three values for
the magnetic quantum number. That means we get three
different orientations. We already said that
when l is equal to one, we're talking about a p orbital. A p orbital is shaped
like a dumbbell here, so we have three possible orientations for a dumbbell shape. If we went ahead and mark these axes here, let's just say this is x axis, y axis, and the z axis here. We could put a dumbbell
on the x axis like that. Again, imagine this as being a volume. This would be a p orbital. We call this a px orbital. It's a p orbital and
it's on the x axis here. We have two more orientations. We could put, again, if this is x, this is y, and this is z, we could put a dumbbell
here on the y axis. There's our second possible orientation. Finally, if this is x,
this is y, and this is z, of course we could put a dumbbell
on the z axis, like that. This would be a pz orbital. We could write a pz orbital here, and then this one right
here would be a py orbital. We have three orbitals, we
have three p orbitals here, one for each axis. Let's go to the last quantum number. The last quantum number is
the spin quantum number. The spin quantum number is m sub s here. When it says spin, I'm going
to put this in quotations. This seems to imply that an electron is spinning on an axis. That's not really what's happening, but let me just go ahead
and draw that in here. I could have an electron ... Let me draw two different versions here. I could have an electron
spin like a top, if you will, this way, or I could have an electron spin around that axis going this way. Again, this is not actually
what's happening in reality. The electrons don't really
spin on an axis like a top, but it does help me to think about the fact that we have two possible values for this spin quantum number. You could spin one way, so we could say the spin quantum number is equal to a positive one-half. Usually you hear that called spin up, so spin up, and we'll symbolize this with an arrow going up
in later videos here. Then the other possible value for the spin quantum number, so the spin quantum number is equal to a negative one-half. You usually hear that
referred to as spin down, and you could put an arrow going down. Again, electrons aren't really spinning in a physical sense like this, but, again, if you think
about two possible ways for an electron to spin, then you get these two different, these two possible spin quantum numbers, so positive one-half or negative one-half. Those are the four quantum numbers, and we're going to use those to, again, think about electrons in orbitals.