How many electrons are in #n = 2#? What about #n = 4, l = 3#? What about #n = 6, l = 2, m_l = -1#?
1 Answer
Here's what I got.
Explanation:
Since the question is a bit ambiguous, I will assume that you're dealing with three distinct sets of quantum numbers.
In addition to this, I will also assume that you're fairly familiar with quantum numbers, so I won't go into too much details about what each represents.
#1^"st"# set# -> n=2#
The principal quantum number,
The number of orbitals you get per energy level can be found using the equation
#color(blue)("no. of orbitals" = n^2)#
Since each orbital can hold amaximum of two electrons, it follows that as many as
#color(blue)("no. of electrons" = 2n^2)#
In this case, the second energy level holds a total of
#"no. of orbitals" = n^2 = 2^2 = 4#
orbitals. Therefore, a maximum of
#"no. of electrons" = 2 * 4 = 8#
electrons can share the quantum number
#2^"nd"# set#-> n=4, l=3#
This time, you are given both the energy level,
Now, the subshell is given by the angular momentum quantum number,
#l=0 -># the s-subshell#l=1 -># the p-subshell#l=2 -># the d-subshell#l=3 -># the f-subshell
Now, the number of orbitals you get per subshell is given by the magnetic quantum number,
#m_l = -l, ..., -1, 0, 1, ..., +l#
#m_l = {-3; -2; -1; 0; 1; 2; 3}#
So, the f-subshell can hold total of seven orbitals, which means that you have a maximum of
#"no. of electrons" = 2 * 7 = 14#
electrons that can share these two quantum numbers,
#3^"rd"# set#-> n=6, l=2, m_l = -1#
This time, you are given the energy level,
Since you know the exact orbital, it follows that only two electrons can share these three quantum numbers, one having spin-up,