Quantum Numbers: Magnetic Quantum Number - Online Tutor, Practice Problems & Exam Prep

The magnetic quantum number ($m_l$) is crucial for understanding the orientation and location of electrons within an atom's orbitals. It arises from the angular momentum quantum number ($l$), indicating the shape and energy level of the orbital. The $m_l$ values range from $-l$ to $+l$, including all whole numbers in between, which correspond to the specific orbitals within a subshell. For instance, if $l$ is 2, $m_l$ can be $-2$, $-1$, $0$, $+1$, or $+2$. These values help to identify the orbital's numerical location, with s subshells having one orbital, p subshells three, d subshells five, and f subshells seven, leading to a maximum electron capacity of 2, 6, 10, and 14 respectively. This concept is foundational for understanding electron configurations and will be further explored when discussing the spin quantum number.

Quantum Numbers: Magnetic Quantum Number

Now the magnetic quantum number deals with orbitals, and recall that an orbital is the region within a sub shell where two specific electrons can be found, not an orbital. Gives us quite a bit of information. It tells us the energy level of the electron, but it also gives us details on the shape of the orbitals for those electrons.

So we can see from this that the orbital which is connected to your magnetic quantum number has its origins in our n quantum number and our l quantum number. Now that we see this connection, move on to the next video and let's take a look at an example question.

Quantum Numbers: Magnetic Quantum Number Example 1

Here we have to provide the identity of a set of orbitals that exist in the fourth principle level and F sublevel. All right, So they're telling us that it exists in the fourth principle level, which means it's connected to our principal quantum number N. Since it says 4th, that means N is 4.

And then they're giving us the sub level letter which is F which would mean that we're dealing with a 4F set of orbitals. That would mean that option C would have to be our correct answer.

Quantum Numbers: Magnetic Quantum Number

The magnetic quantum number which uses M_l as its variable equals the orientation of the orbitals. Now this is a little bit vague, but what exactly does it mean? Well, it just gives us the location of the electrons. Now, like the other quantum numbers that we've seen before with N and L, M_l has its own limitation. It is the range of the angular momentum quantum number L, meaning that if L were equal to let's say 2, M_l is equal to the range of two, meaning that it's equal to -2 to +2, all the whole number integers in between. So it would be equal to -2, -1, 0, +1, and +2.

If we take a look down here, we have our subshell letters S, P, D, and F. If we know our subshell letters, then we know what the L value will be. If we know what the L value is, then we know what M_l is because again it's the range of L. When L is 0, there's no such thing as ±0, so M_l is 0. When L is 1, M_l = -1 to +1. So all the numbers in between and we just said if L = 2, M_l = -2 to +2 and then if L is 3 then M_l is -3 to +3.

Now how do these numbers relate to the location of electrons? Well, remember, if you're an S subshell, you have one orbital associated with yourself which is in the shape of the sphere. Here, this orange, this red box we say represents our orbital. It has a number designation. That number designation matches the M_l value, so this would be 0. Here we have -1, 0, and +1. And look, we have 3 orbitals, so this would be -1, 0, and +1. Here -2 to +2. So these are the number designations for each of these orbitals. It gives us their numerical location. And then -3 to +3 represents all of these different orbitals here.

So this is what M_l is telling us. Now what you need to realize here is that with these shapes, we see P_x, we see d_xy, we see F_y^3, 3/5 Y R-squared. It's a lot, but just realize that most orbitals have letter value associated with them, these ones that I circled. But only the numerical values for M_l are important, so -2, +1, etc. We're going to say here the maximum number of electrons in S, P, D, and F subshells. This is important is 2, 6, 10, and 14 electrons. We'll see later on why that is when we talk about the spin quantum number. But for now just realize with each one of these sublevel letters that's how many electrons they can hold at max.

Quantum Numbers: Magnetic Quantum Example 2

Here it says which of the following is not a valid magnetic quantum number for the seven F set of orbitals. So remember here, in order to find our magnetic quantum number values which are M_l, They're based on our L value here. Remember L can be 0, 1, 2, 3 based on the sublevel or subshell letter.

Since the letter here is F, that means L is equal to 3. Since L is equal to three M_l which is the range of it would equal -3 to +3 and all the numbers in between. So these would be all the allowable values for A7F set of orbitals.

The only one that's left out is +4. This would mean that D would be our correct answer. This one should not be one of the valid values for M_l when given a set of seven F orbitals.

How many different values of m_l are possible for a 4d set of orbitals?

• A. 1
• B. 3
• C. 7
• D. 5
• E. 2

Select a correct set of values for an electron found within the designated 5d orbital. 

 

• A. n = 5, l = 2, m_l = 0
• B. n = 5, l = 3, m_l = +1
• C. n = 5, l = 3, m_l = 0
• D. n = 5, l = 5, m_l = – 2
• E. n = 5, l = 2, m_l = +5

Which of the following statements is false?

a) A set of d orbitals contains 5 orbitals.

b) A set of 4s orbitals would have more energy than a set of 3p orbitals.

c) The second shell of an atom possesses d orbitals.

d) A set of f orbitals contains 3 orbitals.

e) The first energy level contains only s orbitals.

• A. a, b
• B. b, d
• C. c, d
• D. d, e
• E. b, e

Here’s what students ask on this topic:

How can I find the magnetic quantum number?

The magnetic quantum number, designated as $m_l$, can be found once you know the orbital angular momentum quantum number, or the azimuthal quantum number, denoted as $l$. For a given value of $l$, which can range from 0 to $n-1$ (where $n$ is the principal quantum number), $m_l$ can take on integer values ranging from $-l$ to $+l$, including zero.

So, if you have an electron in an orbital with $l=2$, the possible values for $m_l$ would be -2, -1, 0, 1, and 2. Each of these corresponds to a different orientation of the orbital in three-dimensional space. Remember that $l$ is related to the shape of the orbital (s, p, d, f corresponding to $l$ values of 0, 1, 2, 3, respectively), and $m_l$ relates to the orientation of that orbital.

What does the magnetic quantum number determine?

The magnetic quantum number, designated as $m_l$, is one of the four quantum numbers that describe the unique quantum state of an electron in an atom. It determines the orientation of the electron's orbital around the nucleus. Specifically, the magnetic quantum number can take on integer values ranging from $-l$ to $+l$, where $l$ is the azimuthal (or angular momentum) quantum number associated with the orbital shape.

For example, if an electron is in a p-orbital, where the azimuthal quantum number $l$ is 1, the magnetic quantum number $m_l$ can have values of $-1$, $0$, or $+1$, corresponding to the three different orientations that a p-orbital can have in space. These orientations are often depicted as the p_x, p_y, and p_z orbitals. The magnetic quantum number is particularly important when considering the effect of an external magnetic field on an electron, as it helps to determine the electron's energy in the presence of that field due to the Zeeman effect.

What is the magnetic quantum number?

The magnetic quantum number, symbolized as $m_l$, is one of four quantum numbers used in quantum mechanics to describe the unique quantum state of an electron. It specifically describes the orientation of an electron's orbital around a nucleus. The magnetic quantum number can take on integer values ranging from $-l$ to $+l$, where $l$ is the azimuthal quantum number or angular momentum quantum number associated with the electron's orbital.

For example, if an electron is in a p-orbital, the azimuthal quantum number $l$ is 1, and thus the magnetic quantum number $m_l$ can have values of $-1$, $0$, or $+1$. These values correspond to the different orientations an electron's orbital can have in a three-dimensional space, which becomes particularly relevant in the presence of a magnetic field, as it leads to the splitting of energy levels, a phenomenon known as Zeeman splitting. The magnetic quantum number helps in understanding the spatial distribution of electrons in an atom and is crucial for predicting the magnetic properties of an atom or molecule.

How can I find the magnetic quantum number?

The magnetic quantum number, designated as $m_l$, can be found once you know the orbital angular momentum quantum number, or the azimuthal quantum number, denoted as $l$. For a given value of $l$, which can range from 0 to $n-1$ (where $n$ is the principal quantum number), $m_l$ can take on integer values ranging from $-l$ to $+l$, including zero.

So, if you have an electron in an orbital with $l=2$, the possible values for $m_l$ would be -2, -1, 0, 1, and 2. Each of these corresponds to a different orientation of the orbital in three-dimensional space. Remember that $l$ is related to the shape of the orbital (s, p, d, f corresponding to $l$ values of 0, 1, 2, 3, respectively), and $m_l$ relates to the orientation of that orbital.