Quantum Numbers Question

[LexyDenaburg_3A]

How do we tell how many quantum numbers specifies a subshell?

[Jay Solanki 3A]

I'm gonna interpret this as a general quantum numbers question. The first number, the principle quantum number n, refers to the exact energy level an electron is located on. The second number is l, which specifies the type of subshell the electron is located in; for this term usually s=0, p=1, d=2, and f=3. The third number ml specifies the specific STATE the electron is located; considering an electron in the p-subshell, for instance, the electron could be in the 2px, 2py, or 2pz state. The range of numbers for ml is usually whole numbers such that -l<0<l (so p would be -1,0,1). The fourth number is the electron spin, which is either +1/2 or -1/2 depending on the electron. This property notes that at most 2 electrons can occupy any STATE in a subshell, but what differentiates them is their electron spin.

I will use the third valence electron of Boron as an example. This electron is located in the 2px state, since electrons occupy the lowest-energy first. In this case, the first quantum number is n=2, the second quantum number is l=1 (for the p subshell), and the third quantum number is ml=-1(for the x state). The electron spin is usually only determined experimentally and varies between boron atoms (if i am not mistaken), and can either be +1/2 or -1/2. For the sake of simplicity, we will assume it is +1/2. I chose this example since it is a bit more varied and I believe that Dr. Lavelle used this same example in his Monday lecture (10/26/20). Hope this helps!

[Jiwon_Chae_3L]

If I'm understanding your question correctly, it depends on how specific of a range that you are given to determine the number of possible quantum numbers. For instance, if you are given the quantum number of an electron, down to the most specific subset, the ms, there is only one specific quantum number that can be used to describe that specific electron. However, if you are given a quantum number such as the ml, l, or n, then you would have to count how many possible positions that any given electron could occupy under that category, like Jay said.