How many electrons are in #n=3#, #l= 2#?

1 Answer
Jun 12, 2017

Answer:

#"10 e"^(-)#

Explanation:

The idea here is that you must use the value of the angular momentum quantum number, #l#, which tells you the energy subshell in which an electron resides, to find the possible values of the magnetic quantum number, #m_l#.

The number of values that the magnetic quantum number can take tells you the number of orbitals that are present in a given subshell.

figures.boundless.com

So, you know that the magnetic quantum number depends on the value of the angular momentum quantum number

#m_l = {-l, -(l-1), ..., -1, color(white)(-)0, +1, ..., +(l-1), +l}#

In your case, you have #l=2#, which is an accepted value for the angular momentum quantum number given the fact that the principal quantum number, #n#, is equal to #3#, so you can say that

#m_l = {-2, -1, color(white)(-)0, +1, +2}#

This tells you that the #d# subshell, which is denoted by #l=2#, holds a total of #5# orbitals.

Since each orbital can hold a maximum of #2# electrons, one having spin-up and one having spin-down, you can say that you have

#5 color(red)(cancel(color(black)("orbitals"))) * "2 e"^(-)/(1color(red)(cancel(color(black)("orbital")))) = "10 e"^(-)#

Therefore, a maximum number of #10# electrons can share these two quantum numbers in an atom.

#n=3, l=2#

These electrons are located on the third energy level, in the #3d# subshell.