Hi everyone,
There may be a simple explanation but I am confused on how the solutions manual gets the answers for how many electrons can have the following quantum numbers in an atom:
For example:
(a) n=2, l=1 there are six electrons
(b) n=4, l=2, m=-2 there are two electrons
(c) n=2 there are eight electrons
(d) n=3, l=2, m=+1 there are two electrons
Could someone explain how are they getting these numbers of electrons? Thanks!
Chapter 2 Question 29 [ENDORSED]
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Tara_Shooshani_3N
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Re: Chapter 2 Question 29
I'll go part by part to explain where the numbers come from:
a) when l=1, we know it is a p-orbital, and 6 electrons can fit in a p-orbital, so the answer is 6.
b) and d) in any m group there are always only 2 electrons maximum. One has upward spin, one has downward.
c) when n=2, l can be either 0 or 1. l=0 means the s-orbital, which can hold 2 electrons, and l=1 is the p-orbital, which hold maximum 6 electrons. 2+6=8
a) when l=1, we know it is a p-orbital, and 6 electrons can fit in a p-orbital, so the answer is 6.
b) and d) in any m group there are always only 2 electrons maximum. One has upward spin, one has downward.
c) when n=2, l can be either 0 or 1. l=0 means the s-orbital, which can hold 2 electrons, and l=1 is the p-orbital, which hold maximum 6 electrons. 2+6=8
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Christopher Reed 1H
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Re: Chapter 2 Question 29 [ENDORSED]
Hi!
I know someone has already kindly answered your question, but I thought you might like another explanation. (:
A. Though the problem gives you n, you only really need l to find the number of electrons in this case. Ml is all the integral values of l, in this case -1, 0, 1. In each of these suborbitals there can be an electron spinning up and one spinning down. With some multiplication (2 x 3 = 6) you find there are 6 electrons.
B. Part B has narrowed your parameters. Now you know the Ml has a specific value. Regardless of this it can only hold 2 electrons; one spinning up and one spinning down.
C. When simply given an energy level, there's a neat trick to help you calculate the number of electrons in it. It turns out the 2n^2 tells you the total number of electrons in an energy level. This is derived from the fact the n^2 tells you the total number of orbitals and that each orbital can only hold 2 electrons. Applying this formula we see that there are 8 electrons.
D. Last one! This is just like part B. Since only one value of Ml is specified you know there can only be 2 electrons.
I hope that by reading both the excellent answer above and my own you understand this concept. Please ask for clarification if needed!
I know someone has already kindly answered your question, but I thought you might like another explanation. (:
A. Though the problem gives you n, you only really need l to find the number of electrons in this case. Ml is all the integral values of l, in this case -1, 0, 1. In each of these suborbitals there can be an electron spinning up and one spinning down. With some multiplication (2 x 3 = 6) you find there are 6 electrons.
B. Part B has narrowed your parameters. Now you know the Ml has a specific value. Regardless of this it can only hold 2 electrons; one spinning up and one spinning down.
C. When simply given an energy level, there's a neat trick to help you calculate the number of electrons in it. It turns out the 2n^2 tells you the total number of electrons in an energy level. This is derived from the fact the n^2 tells you the total number of orbitals and that each orbital can only hold 2 electrons. Applying this formula we see that there are 8 electrons.
D. Last one! This is just like part B. Since only one value of Ml is specified you know there can only be 2 electrons.
I hope that by reading both the excellent answer above and my own you understand this concept. Please ask for clarification if needed!
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danae_blodgett_1H
- Posts: 18
- Joined: Sat Jul 23, 2016 3:00 am
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