Since the concern is a little ambiguous, I will certainly assume the you"re taking care of three unique sets the quantum numbers.

In enhancement to this, i will likewise assume that you"re relatively familiar v quantum numbers, so i won"t get in too lot details around what every represents.

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#1^"st"# set # -> n=2#

The principal quantum number, #n#, tells you the power level on i m sorry an electron resides. In order to be able to determine how many electrons can share this value of #n#, you need to determine specifically how plenty of orbitals you have actually in this power level.

The number of orbitals you acquire per energy level have the right to be uncovered using the equation

#color(blue)("no. Of orbitals" = n^2)#

Since each orbital can hold amaximum of two electrons, it adheres to that as numerous as

#color(blue)("no. Of electrons" = 2n^2)#

In this case, the second energy level hold a full of

#"no. That orbitals" = n^2 = 2^2 = 4#

orbitals. Therefore, a maximum of

#"no. That electrons" = 2 * 4 = 8#

electrons deserve to share the quantum number #n=2#.

#2^"nd"# set #-> n=4, l=3#

This time, girlfriend are provided both the energy level, #n=4#, and also the subshell, #l=3#, on i beg your pardon the electron reside.

Now, the subshell is provided by the angular inert quantum number, #l#, which deserve to take values varying from #0# come #n-1#.

#l=0 -># the s-subshell#l=1 -># the p-subshell#l=2 -># the d-subshell#l=3 -># the f-subshell

Now, the variety of orbitals you acquire per subshell is provided by the magnetic quantum number, #m_l#, i beg your pardon in this case can be

#m_l = -l, ..., -1, 0, 1, ..., +l#

#m_l = -3; -2; -1; 0; 1; 2; 3#

So, the f-subshell can hold full of seven orbitals, which method that you have actually a best of

#"no. The electrons" = 2 * 7 = 14#

electrons that deserve to share these two quantum numbers, #n=4# and also #l=3#.

#3^"rd"# set #-> n=6, l=2, m_l = -1#

This time, you are provided the energy level, #n=6#, the subshell, #l=2#, and the exact orbital, #m_l = 1#, in i m sorry the electrons reside.


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Since you recognize the exact orbital, it adheres to that just two electrons can share these three quantum numbers, one having spin-up, #m_s = +1/2#, and also the other having actually spin-down, #m_s = -1/2#.