Finding Total Number of Electron States with n=3

  • Thread starter Thread starter roeb
  • Start date Start date
  • Tags Tags
    Electron States
AI Thread Summary
For n = 3, the quantum numbers l can be 0, 1, or 2, leading to m values of -l to +l for each l. The calculations show that for l = 2, there are 5 states; for l = 1, there are 3 states; and for l = 0, there is 1 state, totaling 9 states. Each of these states can be occupied by two electrons due to spin, resulting in 18 total electron states. The confusion arises from not accounting for the spin multiplicity correctly in the initial calculation. Understanding the labeling of each independent quantum state clarifies the total count.
roeb
Messages
98
Reaction score
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?
 
Physics news on Phys.org
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:

\psi_{n,l,m}: \psi_{3,0,0} \neq \psi_{3,1,-1} \neq \psi_{3,1,0}

and so on..
 
Last edited:
Thread 'Voltmeter readings for this circuit with switches'
TL;DR Summary: I would like to know the voltmeter readings on the two resistors separately in the picture in the following cases , When one of the keys is closed When both of them are opened (Knowing that the battery has negligible internal resistance) My thoughts for the first case , one of them must be 12 volt while the other is 0 The second case we'll I think both voltmeter readings should be 12 volt since they are both parallel to the battery and they involve the key within what the...
Thread 'Correct statement about a reservoir with an outlet pipe'
The answer to this question is statements (ii) and (iv) are correct. (i) This is FALSE because the speed of water in the tap is greater than speed at the water surface (ii) I don't even understand this statement. What does the "seal" part have to do with water flowing out? Won't the water still flow out through the tap until the tank is empty whether the reservoir is sealed or not? (iii) In my opinion, this statement would be correct. Increasing the gravitational potential energy of the...
Back
Top