Chapter 2 Question 29  [ENDORSED]

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Lexy Swenson 1F
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Joined: Fri Jul 22, 2016 3:00 am

Chapter 2 Question 29

Postby Lexy Swenson 1F » Mon Oct 17, 2016 10:30 pm

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!

Tara_Shooshani_3N
Posts: 29
Joined: Wed Sep 21, 2016 3:00 pm

Re: Chapter 2 Question 29

Postby Tara_Shooshani_3N » Mon Oct 17, 2016 10:38 pm

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

Christopher Reed 1H
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Re: Chapter 2 Question 29  [ENDORSED]

Postby Christopher Reed 1H » Mon Oct 17, 2016 10:52 pm

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!

danae_blodgett_1H
Posts: 18
Joined: Sat Jul 23, 2016 3:00 am

Re: Chapter 2 Question 29

Postby danae_blodgett_1H » Tue Oct 18, 2016 11:09 am

I had the same question. This clears everything up for me. Thank you!


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