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

The angular momentum quantum number (l), a crucial aspect of atomic structure, defines the shape of an atom's orbitals and is always less than the principal quantum number (n), following the rule:

$l=0ton-1$

Each subshell, denoted by the letters s, p, d, and f, corresponds to l values of 0, 1, 2, and 3, respectively. The s subshell is spherical, p subshells have dumbbell-shaped orbitals, d subshells have clover-shaped orbitals with one unique dumbbell with a ring, and f subshells have complex shapes like pacifiers and double clovers. Understanding these subshell shapes is essential for grasping electron configuration and orbital geometry within an atom.

Quantum Numbers: Angular Momentum Quantum Number

The angular momentum quantum number, also known as the azimuthal quantum number, uses the variable L and it equals the shape of the atom, so it gives us its shape. We're going to say the relationship between N and L is that when given the principal quantum number N, L equals 0 up to N - 1 because L has that N - 1 part to it.

The limitation is that the angular momentum quantum number L is always less than the principal quantum number N. So just remember that limitation when it comes to creating a relationship between your N quantum number and your L quantum number.

Quantum Numbers: Angular Momentum Quantum Number Example 1

Here it says what are all possible values for L when n = 4. All right, so remember when N is given, L = 0 up to n - 1. Since N is 4, that means that's 4 -, 1. So that's three.

Three is not your answer though, because we just said L = 0 up to N -1. So L would equal 0 up to three, which means that when L when N is 4L can equals 0, 1-2 or three, meaning that option D is our correct answer.

Quantum Numbers: Angular Momentum Quantum Number

When it comes to the relationship of the quantum number L and a subshell, we say that the shell of an atom can be further divided into subshells, also sometimes called sublevels, with each one assigned a variable letter. We're going to say the value for the angular momentum quantum number L can determine this subshell letter.

So here if we look we have values for L as 0, 1, 2, and 3. When L=0, the subshell letter is S. When L=1, then it's P. When L=2, it's D, and when L=3, it's F. So just remember if you know the L value, you know the subshell letter.

If you know the subshell letter, then you know what your L value will be. So just remember the order in terms of each of these subshell letters and the number associated with them.

Quantum Numbers: Angular Momentum Quantum Number Example 2

Here it says what are the possible values for NNL for an electron found in the third principal level and D sub level. Alright, so here they're saying third principle level. That means third shell. If we're talking about principle, we're talking about our end quantum number. So this would be N=3.

And then remember if we know the sub shell letter or sub level letter we know what L is. Remember here 0,1,2,                                                                                                                                                                                                                                                                                                                                                                                                                                                 </

Provide all the possible values of l for a 2 energy level.

• A. 0
• B. 0, 1
• C. 0, 1, 2
• D. 0, 1, 2, 3
• E. 1

How many sublevels are contained in the third shell (n = 3) for a given atom?

• A. 1
• B. 2
• C. 3
• D. 4
• E. 5

Quantum Numbers: Angular Momentum Quantum Number

Now we say here that the angular momentum quantum number gives information on the shape of the orbitals that electrons occupy. So remember, if your L value is 0, the subshell or sub level would be S. It has a spherical shape, so it's shaped like a sphere.

When we're dealing with l = 1, we're dealing with the P subshell. P has three shapes associated with it, and here we can call them... or dumbbells. So we have 3 dumbbells. When L = 2, the subshell letter is D. This one has five shapes associated with it. The first four are four-leaf clovers and then the last one is an... with a circle around it or a dumbbell with a ring around it.

Then finally, when L = 3, the subshell letter is and it has seven shapes associated with it. The first three are a little bit weird. OK, so here I like to call them pacifiers. So it's a pair of pacifiers for the 1st 3 shapes, and then the next ones 444 leaf clovers. So 44 leaf clovers. And there's four of them, right?

So just remember, when it comes to the angular momentum quantum number, it can also give us information on the shapes of the different orbitals that the electrons can occupy, and these would be the shapes in which the subshell electrons would take.

Quantum Numbers: Angular Momentum Quantum Number Example 3

So here it says, based on the following atomic orbital shape, which of the following set of quantum numbers is correct. All right, so here they're showing us in... with a ring or a circle around it in the middle. We would know that that particular shape is when we're dealing with the subshell letter of D. And remember, if you're dealing with a subshell letter of D, that means L=2. So automatically A&B are out sore answers, either CD or east.

How do we tell what's the best answer? Remember there's a limitation or a connection between N&L. Remember L=0 up to N-1, right? So this tells us that L must always always be a number less than north, right? Because of this N-1 portion here. So here first of all C doesn't work because N also has its own limitation where it's a number from one to Infinity and can't ever equal 0.

Here D doesn't work because here it's saying that N&L are the same value. We just said that a limitation on L is that L must always be a number less than north because of this N-1 portion. So D doesn't work. The best answer would be EN can equal 5L has to be two because it's connected to the subshell D which is connected to this shape. And here L is also less than the value of N. So here E would be our best answer.

Which of the following orbitals possesses the most orbital shapes?

• A. 2p
• B. 7s
• C. 4d
• D. 5p
• E. 5f

Here’s what students ask on this topic:

Which characteristic is given by the angular momentum quantum number?

The angular momentum quantum number, often represented by the letter 'l', determines the shape of an electron's orbital within an atom. It is one of four quantum numbers used to describe the unique quantum state of an electron. The angular momentum quantum number can take on any integer value from 0 to $n-1$, where 'n' is the principal quantum number associated with the electron's energy level.

For a given energy level ($n$), 'l' defines the subshells or sublevels that are present, such as s (sharp), p (principal), d (diffuse), and f (fundamental), corresponding to 'l' values of 0, 1, 2, and 3, respectively. Each of these subshells has a distinct shape, which in turn affects the distribution of electron density around the nucleus. For instance, s orbitals are spherical, while p orbitals are dumbbell-shaped. The angular momentum quantum number is crucial for determining the allowed shapes for an electron's probability cloud within an atom and plays a key role in the chemical bonding and properties of elements.

How can I find the angular momentum quantum number?

The angular momentum quantum number, often represented by the letter 'l', is a quantum number that determines the shape of an electron's orbital and contributes to the angular momentum of an electron within an atom. It can be found by considering the principal quantum number 'n' of the electron's orbital. The angular momentum quantum number 'l' can take on any integer value from 0 to (n-1).

For example, if an electron is in the second energy level (n=2), the possible values of 'l' can be 0 or 1. These values correspond to different types of orbitals: 'l' = 0 is an s-orbital (spherical), 'l' = 1 is a p-orbital (dumbbell-shaped), and so on for higher values of 'l' (d-orbitals for 'l' = 2, f-orbitals for 'l' = 3, etc.).

To find the angular momentum quantum number, you need to know the principal quantum number of the electron's orbital and then list out the possible 'l' values within the range 0 to (n-1). Each of these values of 'l' will correspond to a different orbital shape within that energy level.

What is the angular momentum quantum number?

The angular momentum quantum number, often symbolized as l, is a quantum number that determines the shape of an electron's orbital within an atom. It is one of four quantum numbers used to describe the unique quantum state of an electron. The angular momentum quantum number can take on any integer value from 0 to n-1, where n is the principal quantum number associated with the electron's energy level.

For a given energy level (n), l defines the subshell or sublevel in which the electron resides, with each subshell corresponding to a different shape of the orbital. For example, if l = 0, the orbital is spherical and is called an s orbital. If l = 1, the orbital is dumbbell-shaped and is known as a p orbital. Higher values of l correspond to d and f orbitals, which have more complex shapes.

The angular momentum quantum number is crucial for determining the allowed orbits for electrons in atoms and thus plays a key role in the structure and behavior of atoms in chemical reactions and physical processes.