Possible electrons for an atom

[705676154]

How do you know how many electrons could be in an atom based of given quantum numbers?

[katrinahuwang_1L]

The principle quantum number (n) determines the energy shell. The angular momentum quantum number (l) determines the subshell. So if you're given n = 2 and l = 1, that indicates the 2p subshell. The p subshell has 3 orbitals, and each orbital can hold a maximum of 2 electrons, so the 2p subshell can hold a maximum of 6 electrons. You have to look to the shell and subshell to determine how many orbitals you're dealing with, and from there, you can figure out the number of electrons.

[Sujin Lim 1H]

The answer here depends on which quantum number you are talking about. If we are talking about the principle quantum number, for example, is n=1, there can be only one possible value of l (angular momentum quantum number), which is l=0 (s-orbital). If l=0, the only possible ml (magnetic quantum number) value is ml=0. The spin magnetic quantum number (ms) is always two values -1/2 and +1/2. Therefore, if we ask how many electrons can be in an atom for n=1, we say that there only can b 2 electrons. (n=1 consists of only the s-orbital which has only one orientation, consisting of a spin up and spin down electron).
When n = 2:
l = 0, 1
for l=0, ml=0
for l=1, ml=-1,0,+1
for each ml value, ms = +1/2 and -1/2
Since there are a total of four ml values/orientations in n=2, there are a total of 2*4 = 8 electrons found in n=2.

The same pattern would repeat for n=3, n=4, etc.
If we want to know the number of atoms in a specific ml quantum number, though, there would always be 2 electrons, regardless of the specified n or l value. I hope this makes sense!
I would recommend looking over Figure 1D.3 and Table 1D.2 on the ebook under Topic 1D: The Hydrogen Atom for further clarification and better visualization of what I explained above!