The Electron Configuration: Quantum Numbers: Videos & Practice Problems

Understanding quantum numbers is essential for determining the location and energy levels of electrons within an atom. The principal quantum number (n) indicates the size and energy of an electron shell, with higher numbers representing electrons in outer shells. The angular momentum quantum number (l), also known as the azimuthal quantum number, defines the shape of orbitals (s, p, d, f) within a subshell, with values of 0 for s, 1 for p, 2 for d, and 3 for f. The magnetic quantum number (m_l) specifies the orientation of an orbital within a subshell, with possible values ranging from -l to +l. Lastly, the spin quantum number (m_s) indicates the spin of an electron within an orbital, either +1/2 for up-spin or -1/2 for down-spin. These quantum numbers collectively describe an electron's unique position in an atom, adhering to the Aufbau principle which dictates the order of electron filling in orbitals.

Electron Configuration and Number of Electrons

In order to relate the quantum numbers to an electron configuration, it's first important to know how to number the electrons within an electron orbital diagram. We're going to say here that electrons within configurations are numbered in the order they are written based on the aufbau principle.

So remember, with the aufbau principle we start out with 1S orbital and we move onward, so 1S, then 2S, then 2P and so on. Knowing this, order is the key to numbering the electrons correctly, and from there we'll be able to link the quantum numbers to them.

Electron Configuration and Number of Electrons Example

Here we need to determine the number of the electron highlighted within the electron orbital diagram. So if we look this is what 1S22S22P63S23P4 and we're looking at this electron. Here, we have to determine its number. All right, so we number it in the order of the off file principle.

So we start out with 1S2, so we start numbering them first. So one up, SO11 down to one up, three one down 4. Now 2P6. These are degenerate orbitals, They have the same energy. So following Hun's role we have build them first. So this would be up, up, up. So I number them 567. Then we came back around 8910.

Now we're at 3's again, so 1112, three P orbitals, they're degenerate, same energy again, so half fill according to Hun's rule 13141516. And we can see here that this electron that's highlighted is the 14th electron. So remember, that's the way we're able to number the electrons within an electron orbital diagram. This is key for later on connecting it to the quantum numbers.

Quantum Numbers Review

So here we're going to have a quick review of the quantum numbers. So we're going to say, remember the quantum numbers are a set of values describe the energy levels and ultimately the location of a specific electron. Now here with our principal quantum number, our first one, its variable is N. It describes the size and energy of a shell. So for example, let's say we're dealing with a set of 7D orbitals. Because the number is 7, that means we're dealing with electrons in the 7th shell and therefore n=7.

The angular momentum quantum number, also called the azimuthal quantum number, uses the variable L. It gives us the shape of an orbital within a sub shell. Here subshells are sub levels. They are represented by the letters of S, P, D, and F. If you know the sublevel or subshell letter, then you know what your L value is. S is 0, P is 1, D is 2, and F is 3.

The magnetic quantum number deals with the variable M sub L. It gives us the location of electrons within a set of orbitals. So for example, let's say we're dealing again with 7D orbitals. Remember that your D sub level has five orbitals involved. Each of those orbitals has a number designation. So here this would be -2, -1, 0, +1, and +2. So those numbers are the M sub L values. They are the numerical location of each of these orbitals, and within each of those orbitals we have electrons.

Finally, we have our spin quantum number which is M sub S. It gives us the spin of an electron within an orbital. Remember an orbital can hold a maximum of two electrons. One spins up and would have an M sub S value of +12. The other one spins down and would have an M sub S value of -12.

So this is a crash course in quantum numbers if you didn't get a chance to look at my earlier videos. If you haven't, I highly suggest you go back and take a look. Quantum numbers can be a bit tricky, so it's important to understand these fundamental ideas on how they relate to the ultimate location of an electron within a given atom.

Quantum Numbers and Electron Configuration Example

Here it says give the set a full quantum numbers for the 6th electron of the oxygen atom. So here it says provide the electron orbital diagram for the element or ion. All right. So oxygen atom means oxygen is neutral. Oxygen has an atomic number of 6 here. Its electron configuration would be 1 S 2 2S²2P⁴, filling in this electron orbital diagram 1S²SO1UP1 down to S²1UP1 down.

The next 4 electrons are found within our 2P set of orbitals. Since they're all 2P electrons, they all have the same energy. So following Hun's rule, we half fill first up, up, up and here is my 7th or my 4th electron. Now Step 2. Use the number and letters for the set of orbitals to determine its N and L values. All right, so we're looking for the 6th electron. So this is 1234, half built, 1st 567, and then back around 8:00. So our 6th electron is right here.

All right, So we're going to say here that that electron that we're looking at, it is within a two set of orbitals. Because the number is 2, N equals 2. Because the letter is P, that means l = 1. Remember, if you know the sublevel letter, then you know what L is. So if it's PL. Is 1. Next, locate the specific orbital for the electron to determine its M sub L value. The electron we're looking at is in the 0 orbital that is equal to the M sub L and then finally determine if the electron spins up or spins down to determine the M sub S value it is pointing up.

That means M_s = + 12. So the four quantum numbers for the 6th electron with an oxygen would be n = 2, L equals one, M sub l = 0 and M sub s = + 12. But remember, we can't do this unless we're able to correctly number the electrons as they appear within the electron orbital diagram.

Give the set of four quantum numbers that represent the indicated electron in each of the following elements. 
Mg (7th electron) 

• A. n = 2; l = 2; ml = 0; ms = +1/2
• B. n = 2; l = 1; ml = 0; ms = -1/2
• C. n = 2; l = 1; ml = +1; ms = +1/2
• D. n = 2; l = 1; ml = +1; ms = -1/2
• E. n = 2; l = 1; ml = -1; ms = +1/2

Answer: (C)

Give the set of four quantum numbers that represent the indicated electron in each of the following elements. 
Cl^– (18th electron)

• A. n = 3; l = 0; ml = +1; ms = -1/2
• B. n = 3; l = 0; ml = -1; ms = -1/2
• C. n = 3; l = 2; ml = +1; ms = -1/2
• D. n = 3; l = 1; ml = +1; ms = +1/2
• E. n = 3; l = 1; ml = +1; ms = -1/2

Answer: (E)

Give the set of four quantum numbers that represent the indicated electron in each of the following elements. 
Cr³⁺ (21^st electron) 

• A. n = 3; l = 1; ml = 0; ms = -1/2
• B. n = 3; l = 2; ml = 1; ms = -1/2
• C. n = 3; l = 1; ml = 1; ms = +1/2
• D. n = 3; l = 2; ml = 0; ms = +1/2
• E. n = 3; l = 1; ml = 0; ms = +1/2

Answer: (D)

Here’s what students ask on this topic:

What are the four quantum numbers and what do they represent?

The four quantum numbers are the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (m_l), and the spin quantum number (m_s). The principal quantum number (n) indicates the size and energy level of an electron shell, with higher values representing electrons in outer shells. The angular momentum quantum number (l) defines the shape of the orbital within a subshell, with values of 0 for s, 1 for p, 2 for d, and 3 for f. The magnetic quantum number (m_l) specifies the orientation of an orbital within a subshell, with possible values ranging from -l to +l. The spin quantum number (m_s) indicates the spin of an electron within an orbital, either +1/2 for up-spin or -1/2 for down-spin.

How do you determine the electron configuration using the Aufbau principle?

The Aufbau principle states that electrons fill orbitals starting from the lowest energy level to the highest. To determine the electron configuration, begin with the 1s orbital and proceed to higher orbitals in the order of increasing energy: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so on. Each orbital can hold a specific number of electrons: s orbitals hold 2, p orbitals hold 6, d orbitals hold 10, and f orbitals hold 14. By following this order and filling each orbital according to its capacity, you can determine the electron configuration of an atom.

What is the significance of the magnetic quantum number (m_l)?

The magnetic quantum number (m_l) specifies the orientation of an orbital within a subshell. It determines the number of orbitals and their spatial orientation in a given subshell. The possible values of m_l range from -l to +l, where l is the angular momentum quantum number. For example, if l = 2 (d subshell), m_l can be -2, -1, 0, +1, or +2, corresponding to the five d orbitals. This quantum number is crucial for understanding the distribution of electrons in different orbitals and their magnetic properties.

How do the quantum numbers relate to the electron configuration of an atom?

Quantum numbers provide a unique address for each electron in an atom, describing its energy level, shape, orientation, and spin. The principal quantum number (n) indicates the electron's shell, the angular momentum quantum number (l) specifies the subshell and shape of the orbital, the magnetic quantum number (m_l) defines the orbital's orientation, and the spin quantum number (m_s) indicates the electron's spin direction. By following the Aufbau principle and using these quantum numbers, we can determine the electron configuration, which shows the arrangement of electrons in an atom's orbitals.

What is the role of the spin quantum number (m_s) in electron configuration?

The spin quantum number (m_s) indicates the spin direction of an electron within an orbital. It can have two possible values: +1/2 for an up-spin and -1/2 for a down-spin. Each orbital can hold a maximum of two electrons, and they must have opposite spins to comply with the Pauli exclusion principle. This principle states that no two electrons in an atom can have the same set of four quantum numbers. The spin quantum number helps in determining the specific arrangement of electrons within orbitals and ensures that electrons are paired correctly within each orbital.