Sapling HW number 25

[Sarah Huang 3A]

Hi everyone!

I was wondering if anyone can explain how to use the quantum numbers for n, l and ml because I am lost on how to use them. I know that l has 0,1,2,3, which correspond with s,p,d,f, but how do you determine ml? Since I don't have a great understanding of this concept, I can't really do the problems regarding this on the sapling

[John Pham 3L]

N is the principal quantum number. It represents the shell and energy of an orbital in an atom. It can have the values n = 1, 2, 3, ... etc

L is the angular momentum quantum number. It represents the subshell and the type of orbital. It can have the values from l = 0 to l = n - 1
S-orbital would be l =0, P-orbital would be l = 1, D-orbital would be l = 2, and F-orbital would be l = 3

Example: What values of L are possible if N = 4?
Use L = N -1 to find the highest value of L
In this case, we could have a value of L = 3 which is the F-orbital
N = 4 could then have L equal to 0, 1, 2, or 3


Ml is the magnetic quantum number. It distinguishes the individual orbitals within the subshell. It can have the values Ml = -L, L -1, ..., +L
For subshell L, there are 2L + 1 different values of ML.

Example: How many orbitals would L = 1 have?
Plug this into the equation 2L + 1
You would see that there are 3 orbitals total when L = 1
ML could be -1, 0, or 1. Each of these values represents a specific orientation of a given orbital.

You could also think about this with an electron configuration.
We know that the s-orbital can hold 2 e- so it would be 1 orbital, the p-orbital holds 6 e- so it would be 3 orbitals, the d-orbital holds 10 e- so it would be 5 orbitals, and the f-orbital holds 14 e- so it would be 7 orbitals.

[DavidTabib 3H]

Thank you so much. This answered my question as well!

[Sarah Huang 3A]

John, thank you so much!