I was wondering how to find the amount of electrons in an atom when given the two quantum numbers n and l.
For example if the question was : how many electrons are in an atom with the following two quantum numbers, n= 3 and l= 2?
How would I go about determining this?
Determining Amount of Electrons From Quantum Numbers
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Re: Determining Amount of Electrons From Quantum Numbers
The principal quantum number n determines the shell where the electrons are located, and the angular momentum quantum number l describes the shape (s, p, d, f). l can be any value from 0 to n1. Therefore if we are asked how many electrons are in n=3 and l=2, we first try and determine which subshell it's looking for. l=2 corresponds to the d orbital, which can hold a maximum of 10 electrons due to the 5 possible orbital configurations (ml). If l were to equal 1, then we would be looking at the p subshell which can hold a maximum of 6 electrons.

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Re: Determining Amount of Electrons From Quantum Numbers
Unless the problem were specific about what element it is looking for or how many electrons are in the outmost subshell (ex: 3d^{2}), it would probably be too vague to give a clear answer. Perhaps you could give a range of how many electrons there could potentially be?
For example, if the only information given were the quantum numbers n=3 and l=2, we know that the outmost subshell would be 3d. This means there are at least 19 electrons (1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{1}) and at most 28 electrons (1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}).
For example, if the only information given were the quantum numbers n=3 and l=2, we know that the outmost subshell would be 3d. This means there are at least 19 electrons (1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{1}) and at most 28 electrons (1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}).

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Re: Determining Amount of Electrons From Quantum Numbers
No disrespect, but this is wrong. I like breaking down question and relating them to more ordinary questions; so for this specific questions, I relate the electron's quantum number to an address, and the question is asking how many people can live with a given address. For example, who can possibly live at a location with these two parts of an address: State =California and City =Los Angeles. So, obviously residence of San Diego wouldn't count because only the residence of LA can fulfill the given conditions.
The question states "how many electrons are in an atom with the following two quantum numbers, n= 3 and l= 2?". (note: the actual element is irrelevant)
So, in this question number the given quantum numbers narrow down how many electrons can fulfill these conditions. I believe this was your misunderstanding comes from. You answered with all the electrons needed to build up to that energy level (i.e. relating to my example above, that's equivalent to answering with all residence of California). n=3 and l=2 is a conditions for electrons on the 3d orbital. Since all dorbitals can hold a total of 10 electrons the answer is 10!
Here is a good video that cover all 8 possible cases that could come up on a problem like this: http://youtu.be/22vOPpAoxzA
The question states "how many electrons are in an atom with the following two quantum numbers, n= 3 and l= 2?". (note: the actual element is irrelevant)
So, in this question number the given quantum numbers narrow down how many electrons can fulfill these conditions. I believe this was your misunderstanding comes from. You answered with all the electrons needed to build up to that energy level (i.e. relating to my example above, that's equivalent to answering with all residence of California). n=3 and l=2 is a conditions for electrons on the 3d orbital. Since all dorbitals can hold a total of 10 electrons the answer is 10!
Here is a good video that cover all 8 possible cases that could come up on a problem like this: http://youtu.be/22vOPpAoxzA
AhYeon_Kwon_4G wrote:Unless the problem were specific about what element it is looking for or how many electrons are in the outmost subshell (ex: 3d^{2}), it would probably be too vague to give a clear answer. Perhaps you could give a range of how many electrons there could potentially be?
For example, if the only information given were the quantum numbers n=3 and l=2, we know that the outmost subshell would be 3d. This means there are at least 19 electrons (1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{1}) and at most 28 electrons (1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}).
Re: Determining Amount of Electrons From Quantum Numbers
A really simple way to think about this is just knowing that the angular quantum number (l) specifies the subshells. If only n is given you can just use the formula 2(n)^2 to determine the number of electrons. If l is given it can mean multiple things. If l = 0, it is the s orbital, which has 1 subshell and can, therefore, hold two electrons. If l = 1, it is the p orbital, which has 3 subshells and can hold 6 electrons. In this problem, l = 2, which is the d subshell, which has 5 subshells and can hold 10 electrons. This means the answer is 10!
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