# Relationship between quantum numbers atomic orbitals

### Quantum number - Wikipedia

Can somebody explain the basics of Quantum Numbers and Atomic Orbitals? . too bothered about it at your present stage, but that link does oversimplify things. There is a relationship between the motions of electrons in atoms and molecules The quantum numbers provide information about the spatial. The nucleus of a gold atom has an atomic of atomic number, Z = 79, so the Au79 + The energy difference between these energy levels result in the spectral lines of These quantum numbers conspire to give spherical s-orbitals, dumbbell.

The sign of the wavefunction should not be confused with a positive or negative electrical charge. The square of the wavefunction at a given point is proportional to the probability of finding an electron at that point, which leads to a distribution of probabilities in space. The probability of finding an electron at any point in space depends on several factors, including the distance from the nucleus and, in many cases, the atomic equivalent of latitude and longitude.

Describing the electron distribution as a standing wave leads to sets of quantum numbers that are characteristic of each wavefunction. From the patterns of one- and two-dimensional standing waves shown previouslyyou might expect correctly that the patterns of three-dimensional standing waves would be complex.

Fortunately, however, in the 18th century, a French mathematician, Adrien Legendre —developed a set of equations to describe the motion of tidal waves on the surface of a flooded planet. The requirement that the waves must be in phase with one another to avoid cancellation and produce a standing wave results in a limited number of solutions wavefunctionseach of which is specified by a set of numbers called quantum numbers.

Each wavefunction is associated with a particular energy. Because the line never actually reaches the horizontal axis, the probability of finding the electron at very large values of r is very small but not zero. The quantum numbers provide information about the spatial distribution of an electron. Although n can be any positive integer, only certain values of l and ml are allowed for a given value of n.

The Principal Quantum Number The principal quantum number n tells the average relative distance of an electron from the nucleus: A negatively charged electron that is, on average, closer to the positively charged nucleus is attracted to the nucleus more strongly than an electron that is farther out in space.

This means that electrons with higher values of n are easier to remove from an atom. All wavefunctions that have the same value of n are said to constitute a principal shell because those electrons have similar average distances from the nucleus.

As you will see, the principal quantum number n corresponds to the n used by Bohr to describe electron orbits and by Rydberg to describe atomic energy levels. The Azimuthal Quantum Number The second quantum number is often called the azimuthal quantum number l. The value of l describes the shape of the region of space occupied by the electron. For a given atom, all wavefunctions that have the same values of both n and l form a subshell. The regions of space occupied by electrons in the same subshell usually have the same shape, but they are oriented differently in space.

## Quantum numbers

Each wavefunction with an allowed combination of n, l, and ml values describes an atomic orbital, a particular spatial distribution for an electron. 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.

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. This tells us the orientation of that orbital.

The values for ml depend on l.

### Quantum Mechanics and Atomic Orbitals - Chemistry LibreTexts

That sounds a little bit confusing. Let's go ahead and do the example of l is equal to zero. 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? 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's write that down here.

If l is equal to one, what are the allowed values for the magnetic quantum number? 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.

## Quantum number

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.