# Relationship between quantum numbers and electrons

### Quantum Numbers - Chemistry LibreTexts

The significance of the electron spin quantum number is its determination of an atom's. Learn the quantum numbers that are assigned to electrons. from electrified hydrogen gas was equal to the energy difference of the electron's energy states. The nucleus of an atom is surrounded by a cloud of electrons. Discover how these electrons are structured around the nucleus by learning about.

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.

There's only one possible value you could get for the angular momentum quantum number, 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. If n is equal to two, what are the allowed values for l?

Then n minus one would be equal to one. So we have two possible values for l. 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. Now, in the second main energy level, or the second shell, we have another value for l.

When l is equal to one, we're talking about 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.

## Quantum numbers

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.

## Quantum number

This tells us the orientation of that orbital. The values for ml depend on l. 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.

### Quantum numbers (video) | Quantum Physics | Khan Academy

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.

**How To Determine The Maximum Number of Electrons Using Allowed Quantum Numbers - 8 Cases**

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.

- Quantum Numbers

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. This diagram predicts the following order of increasing energy for atomic orbitals.

Electron Configurations, the Aufbau Principle, Degenerate Orbitals, and Hund's Rule The electron configuration of an atom describes the orbitals occupied by electrons on the atom. The basis of this prediction is a rule known as the aufbau principle, which assumes that electrons are added to an atom, one at a time, starting with the lowest energy orbital, until all of the electrons have been placed in an appropriate orbital.

This is indicated by writing a superscript "1" after the symbol for the orbital. The fifth electron therefore goes into one of these orbitals. Does the second electron go into the same orbital as the first, or does it go into one of the other orbitals in this subshell? To answer this, we need to understand the concept of degenerate orbitals. By definition, orbitals are degenerate when they have the same energy. The energy of an orbital depends on both its size and its shape because the electron spends more of its time further from the nucleus of the atom as the orbital becomes larger or the shape becomes more complex.

In an isolated atom, however, the energy of an orbital doesn't depend on the direction in which it points in space. Orbitals that differ only in their orientation in space, such as the 2px, 2py, and 2pz orbitals, are therefore degenerate. Electrons fill degenerate orbitals according to rules first stated by Friedrich Hund.

Hund's rules can be summarized as follows. One electron is added to each of the degenerate orbitals in a subshell before two electrons are added to any orbital in the subshell. Electrons are added to a subshell with the same value of the spin quantum number until each orbital in the subshell has at least one electron. When the time comes to place two electrons into the 2p subshell we put one electron into each of two of these orbitals. The choice between the 2px, 2py, and 2pz orbitals is purely arbitrary.

The electrons in the 2p orbitals on carbon can therefore be represented as follows.