Midterm 2007 review question  [ENDORSED]

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Midterm 2007 review question

Postby Annalia_Ferrer_1F » Sun Oct 30, 2016 4:17 pm

What is the maximum number of electrons in an atom that can have these quantum numbers?

The answer is 25 electrons but I do not understand how you get the answer.

Michael Lesgart 1H
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Re: Midterm 2007 review question  [ENDORSED]

Postby Michael Lesgart 1H » Sun Oct 30, 2016 4:46 pm

When n=5, l can equal 0,1,2,3,4 which corresponds to the s,p,d,f, and (theoretically) g subshells. 5s has one orbital (maximum of 2 electrons), 5p has three orbitals (maximum of 6 electrons), 5d has five orbitals (maximum of 10 electrons), 5f has 7 orbitals (maximum of 14 electrons), and 5g would theoretically have 9 orbitals (maximum of 18 electrons.) I say theoretically because no electron would ever reach the 5g energy state.

So, you also know that the magnetic spin is +1/2. Each orbital has a maximum of two electrons and each electron in that orbital either has a +1/2 spin or a -1/2 spin. In this question, you are only interested in the electrons with a +1/2 spin. So, you know that ONE electron in the 5s orbital will have a +1/2 spin, THREE electrons in the 5p orbital will have a +1/2 spin (remember the rest of the electrons must have a -1/2 spin since half have a +1/2 spin and the other half have -1/2 spin), FIVE electrons in the 5d orbital will have a +1/2 spin, SEVEN electrons in the 5f orbital will have a +1/2 spin, and NINE electrons in the 5g orbital will have a +1/2 spin.

Adding up all the possible electrons with the quantum numbers n=5 and ms=+1/2 gives you 1+3+5+7+9= 25 total electrons

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