How many orbitals are in the 𝑛=5 shell?

Question

How many orbitals are in the 𝑛=5n=5 shell?

Answer 1

For n=5,

we can have l = 4, 3, 2, 1, and 0 (l = n-1).

For each l , we have ml ranging from -l to l.

The total number of ml will tell us the number of orbitals.



l=4, ml=-4,-3,-2,-1,0,1,2,3,4 for a total of 9

l=3, ml=-3,-2,-1,0,1,2,3 for a total of 7

l =2, ml=-2,-1,0,1,2 for a total of 5

l=1, ml=-1,0,1 for a total of 3

l=0, ml=0 for 1

Add all these up and we get 25 orbitals and 50 paired electrons.