Finding Total Number of Electron States with n=3

In summary, for n=3, there are a total of 18 quantum states, with l taking on values of 0, 1, and 2 and m taking on values of -2, -1, 0, 1, and 2. This is due to the fact that there are two quantum states for each combination of l and m, taking into account electron spin. This can be seen by labeling each state as \psi_{n,l,m}.
  • #1
roeb
107
1

Homework Statement


n = 3
Using the fact that there are two quantum states for each value of l and m because of electron spin. Find the total number of electron states with n = 3.


Homework Equations





The Attempt at a Solution


I've already determined that l = 0, 1, 2
and m = -2, -1, 0, 1, 2

So, given the information I figured it would be 8 * 2 = 16 quantum states.
Unfortunately, it's supposed to be 18 quantum states and I fail to see where they pick up 2 extra ones. Does anyone know what I am doing incorrectly?
 
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  • #2
Well for n = 3...

Set l = 2:
then m can take on the range of: -2,-1,0,1,2

Set l = 1:
m = {-1,0,1}

l = 0:
m = 0

There's 9 states.

EDIT: Think of, for n = 3, every independent quantum state by labelling your state:

[tex]\psi_{n,l,m}: \psi_{3,0,0} \neq \psi_{3,1,-1} \neq \psi_{3,1,0}[/tex]

and so on..
 
Last edited:
  • #3



I would suggest double-checking your calculations and equations to ensure accuracy. It is possible that you may have missed a step or made a mistake in your calculations. Another approach could be to consult with a colleague or reference material to verify the correct number of quantum states for n = 3. Additionally, consider the possibility that there may be additional factors or variables that need to be taken into account in order to arrive at the correct answer. It is always important to thoroughly review and analyze data in order to arrive at accurate conclusions in science.
 

What is the formula for finding the total number of electron states with n=3?

The formula for finding the total number of electron states with n=3 is 2n^2 = 2(3)^2 = 18.

How do you determine the number of electron states in each sublevel of n=3?

To determine the number of electron states in each sublevel of n=3, you can use the formula 2l+1, where l is the angular momentum quantum number. For n=3, the sublevels are l=0,1,2, so the number of states in each sublevel is 2(0)+1=1, 2(1)+1=3, and 2(2)+1=5.

Why is the number of electron states with n=3 greater than the number of states with n=2?

The number of electron states with n=3 is greater than the number of states with n=2 because as the principal quantum number increases, the number of sublevels and therefore the number of states in each sublevel also increases. This is due to the fact that as the energy level increases, the orbitals become more complex and can hold more electrons.

Can the total number of electron states with n=3 be calculated for any element?

Yes, the total number of electron states with n=3 can be calculated for any element. This is because the principal quantum number, n, is a fundamental property of the electron and does not vary between elements.

How does the total number of electron states with n=3 relate to the electron configuration of an element?

The total number of electron states with n=3 relates to the electron configuration of an element because it determines the maximum number of electrons that can occupy the n=3 energy level. This number is then used to determine the arrangement of electrons in the sublevels of n=3, which make up the electron configuration of an element.

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