The** Angular Momentum Quantum Number **gives the shape of the atomic orbitals.

Angular Momentum Quantum Number

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## Quantum Numbers: Angular Momentum Quantum Number

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the angular momentum Quantum number, also known as the as a mutual quantum number, uses the variable L. And it equals the shape of the atoms. So it gives us its shape. We're going to say the relationship between N N L. Is that when given the principal quantum number, n l equals zero up two and minus one because l has that end minus one 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 end quantum number and your l quantum not.

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## Quantum Numbers: Angular Momentum Quantum Number Example 1

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here, it says. What are all possible values for L When n equals for All right, So remember when n is given out equals zero up to and minus one since Ennis four. That means that's four minus one. So that's three. Three is not your answer, though, because we just said Al equals zero up to n minus one. So I would equal zero up to three. Which means that when l when Ennis four Alcon equals 012 or three, meaning that option D is are correct answer.

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## Quantum Numbers: Angular Momentum Quantum Number

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when it comes to the relationship of the quantum number l and a sub shell, we say that the shell of an atom can be further divided into sub shelves, also sometimes called sub levels. With each one assigned a variable letter, we're gonna say the value for the angular momentum quantum number l can determine this sub shell letter. So here, if we look, we have values for L as 012 and three when l equals zero, the sub shawl letter is s When al equals one, then it's p when l equals to its d And when l equals three, it's f So just remember, if you know the l value, you know the sub shell letter. If you know the sub shell letter, then you know what your L value will be. Okay, so just remember the order in terms off each of these sub shell letters and a number associated with them

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## Quantum Numbers: Angular Momentum Quantum Number Example 2

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here, it says, What are the possible values for N N L for an electron found in the third principle level and d sub level. Alright, so here they're saying third principle level. That means Third show. If we're talking about principle, we're talking about our end quantum number, so this would be an equals three and then remember, if we know the sub shall letter or sub level letter, we know what Ellis remember here. 012 and three and then our sub level or sub shell letter would be S p d and F since its d. That means the L value has to be to so al equals two. And that would mean that option deed is are correct answer.

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Problem

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

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Problem

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

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concept

## Quantum Numbers: Angular Momentum Quantum Number

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Now we say here that the angular momentum quantum number gives information on the shape of the orbital's that electrons occupied. So remember, if your L value is zero, the sub shell or sub level would be s. It has a satirical shape, so it's shaped like a sphere. When we're dealing with l equals one. We're dealing with the peace. Upshaw P has three shapes associated with it, and here we can call them Ellipses or dumbbells. So we have three dumbbells. When l equals to the sub shall letter is deep. This one has five shapes associated with it. The first four are four leaf clovers. And then the last one is in ellipses with a circle around it, or a dumbbell with a ring around him around it. Then finally, when l equals three, the sexual letter is F, and it has seven shapes associated with it. The first three are a little bit weird. Okay, so here I like to call them passive fires. So it's a pair of passive fires for the first three shapes, and then the next one's four double four leaf clovers. So Double four leaf clovers and there's four of them all 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 orbital's that the electrons can occupy. And these would be the shapes in which the sub shovels sub shall electrons would take.

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## Quantum Numbers: Angular Momentum Quantum Number Example 3

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so here it says, Based on the following atomic orbital shape, which of the following set of quantum numbers is correct? Alright, so here they're showing us in ellipses with a ring or circle around it in the middle, we would know that that particular shape is when we're dealing with the sub shell number on social letter of D. And remember, if you're dealing with a sub Schelotto letter of D, that means l is too so automatically A and B are out sore answers either C, d or E. How do we tell what's the best answer? Remember, there's a limitation or ah, connection between and and l remember l equals zero up to n minus one. Right? So this tells us that l must always, always be a number less than n right. Because of this end minus one portion here. So here, first of all, see, doesn't work because N also has its own limitation, where it's a number from one to infinity and can't ever equals zero here. D doesn't work because here it's saying that an and l are the same value. We just said that a limitation on L is that l must always be a number less than N because of this end, minus one portion so he doesn't work. But best answer would be eat and can equal five. El has to be to because it's connected to the sub shawl D, which is connected to the shape. And here, Alice also less than the value of n so here e would be our best answer.

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Problem

Which of the following orbitals possesses the most orbital shapes?

A

2p

B

7s

C

4d

D

5p

E

5f

Additional resources for Quantum Numbers: Angular Momentum Quantum Number

PRACTICE PROBLEMS AND ACTIVITIES (17)

- The contour representat ion z of one of the orbitals for the n = 3 shell of a hydrogen atom is shown here. (a)...
- The accompanying drawing shows a contour plot for a dyz orbital. Consider the quantum numbers that could poten...
- Identify each of the following orbitals, and give n and l quantum numbers for each. (a) (b)
- (a) For n = 4, what are the possible values of l?
- Give the numerical values of n and l corresponding to each of the following orbital designations: (d) 5d.
- Give the numerical values of n and l corresponding to each of the following orbital designations: (a) 3p.
- What are the possible values of l for each given value of n? a. 1 b. 2 c. 3 d. 4
- Which of the following represent impossible combinations of n and l? (a) 1p (b) 4s (c) 5f (d) 2d
- Which combinations of n and l represent real orbitals, and which do not exist? a. 1s b. 2p c. 4s d. 2d
- Sketch the 1s and 2p orbitals. How do the 2s and 3p orbitals differ from the 1s and 2p orbitals?
- Sketch the shape and orientation of the following types of orbitals: (a) s.
- Sketch the 3d orbitals. How do the 4d orbitals differ from the 3d orbitals?
- (a) The average distance from the nucleus of a 3s electron in a chlorine atom is smaller than that for a 3p el...
- Suppose that in an alternate universe, the possible values of l are the integer values from 0 to n (instead of...
- What do the different colors in the two lobes of the p orbitals specify?
- What is the l quantum of an orbital that has four lobes that resemble a cloverleaf?
- Imagine a universe in which the four quantum numbers can have the same possible values as in our universe exce...