The **Quantum Numbers** can give both the quantity and location of electrons within a given atom.

Quantum Theory & Electrons

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concept

## Quantum Numbers: Number of Electrons

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now remember, an Adam possesses shelves. Each shell forgiven. Adam has a maximum number of electrons it can hold. So here, when only the show number N is given, the number of electrons is equal to two times n squared. So if we're looking here at the first shower n equals one, that would mean that we have two times one squared, which is two times one. So the first shell can hold a maximum of two electrons. The second shell here and equals two B two times two squared, which be two times four, which equals eight electrons. Max that can it can hold. Remember, if they only give you the end value, then you can use two times and square to determine the total number of electrons found within that given show.

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example

## Quantum Numbers: Number of Electrons Example 1

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here we have to determine how many electrons can be found in the seventh shell of an atom. Remember, Seventh Shell corresponds to n equals seven. When we only know the shell number. The number of electrons is just equal to two times n squared without equal two times seven squared seven squared is and multiplying it by two means that we can have, theoretically, up to 98 electrons within the chef. Some shell of a given, Adam. So that would mean that option D would be are correct answer.

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concept

## Quantum Numbers: Number of Electrons

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when we have mawr than just the quantum number and being given to us. Then we must follow this quantum electrons roadmap. So the way it works is they could give us the L value for our electrons. And if we know our l value of our electrons, we can go straight into the number of orbital's involved. Remember, each orbital can hold a total of two electrons, right, so one up and one down. And then all we need to do is from the number of orbital's determine the number of electrons. So since each orbital can hold two electrons, we multiply the number of orbital's by two. And that will give us our number of electrons. Now they could also give you the sub level letter and that would correspond still to my l value. And then you would take the same path. You have your l value. From there, you can determine the number off Orbital's by Isabel, remember, And sable is the range of L. Once you know, your orbital's multiplied by two to get the number of electrons. Now, what else could they do? Well, they could give you your n value here, and if you know, the end value would do end minus one, which would give you all the possible values of L. And again, knowing the L value would give you your m sub l value multiplying that by two. What again give you the total number of electrons. It give me a bit complicated, but click on the next video and let's take a look at example and how we're gonna utilize this quantum electrons roadmap.

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example

## Quantum Numbers: Number of Electrons Example 2

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here, it says, determine the number of electrons that could be found in the seventh shell and D sub low. So Step one tells me to determine the L value. For I went from either a given n value or from a sub shawl or sub level letter here. They're telling me that it's d because it's D. That means that we know that l is going to be, too. If they had just given me an end value in some other quantum numbers, then I would have utilized this part of our map. Now we know L is equal to two. If M Sable is not given, used the L Value to determine the number of Orbital's Remember M. Sobel is the range of AL So M. Sobel would be negative 2 to 2, so negative to negative 10 plus one and plus two that is a total of five orbital's and then, based on the number of orbital's, find the number of electrons. Remember, each orbital can hold a maximum of two electrons. So if I multiply this by two, that means that I have 10 electrons that would be in the seventh shell and have a D sub level letter

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Problem

Determine the number of electrons that can have the following set of quantum numbers:n = 3, m_{l} = 0.

A

2 e

^{-}B

4 e

^{-}C

6 e

^{-}D

3 e

^{-}6

Problem

Determine the number of electrons that can have the following set of quantum numbers:n = 2, m_{s} = –1/2.

A

2 e

^{-}B

4 e

^{-}C

6 e

^{-}D

3 e

^{-}7

Problem

Determine the number of electrons that can have the following set of quantum numbers.

n = 4, l = 3, m_{l} = – 1

A

2 e

^{-}B

4 e

^{-}C

6 e

^{-}D

3 e

^{-}8

Problem

Determine the number of electrons that can have the following set of quantum numbers.

n = 4, m_{L} = – 1, m_{s} = –1/2

A

2 e

^{-}B

4 e

^{-}C

6 e

^{-}D

3 e

^{-}Additional resources for Quantum Numbers: Number of Electrons

PRACTICE PROBLEMS AND ACTIVITIES (3)

- What is the maximum number of electrons that can occupy each of the following subshells? (a) 3s, (b) 2p, (c) 4...
- What is the maximum number of electrons in an atom that can have the following quantum numbers? (a) n = 3, ml...
- What is the maximum number of electrons in an atom whose highest-energy electrons have the principal quantum n...