Homework Question 2.17 part d

[Isa Samad 1L]

Hi there,

I was doing the homework question 2.17 which asks,
How many orbitals are in the subshells with l = to 3

I know that when l = 3, n=4 but wouldn't n=4 have 8 orbitals as there are the 1s,2s,2p,3s,3p,3d,4s,4p orbitals? The solutions manual says there are 7.

Thanks

[Jessica Jones 2B]

When l=3, it corresponds to the f-orbital where there are 14 electrons, 7 orbitals.
l=0 s
l=1 p
l=2 d
l=3 f

[Janice Xiao 1I]

l: 0 1 2 3
orbitals: s p d f
# of orbitals: 1 3 5 7

[Kyra LeRoy 1E]

There are 2(l)+1 orbitals in a subshell of quantum number l. So for D, when l=3, 2(3)+1=7

[Belle Calforda3f]

Since 0 correlates to the S orbitals, 1- p orbitals, 2-d orbitals, and 3- f orbitals, we know that if l = 3 we are referring to the f block. Since the f block has 14 electrons and 7 different orbitals we know there can be 7 subshells. If you memorize what 0,1,2,and 3 correlate to in regards to angular momentum numbers, these types of problems are much easier. We also know that if l=3, then m of l can be -3,-2,-1,0,1,2,3 which is seven values.

[Isabella Zizolfi 2F]

l=0 --> s --> 1 orbital, 2 electrons
l=1--> p --> 3 orbitals, 6 electron
l=2 --> d --> 5 orbitals, 10 electrons
l=3 --> f --> 7 orbitals, 14 electrons