Orbitals

[005321227]

Can anyone help with this problem?

How many orbitals can have the following quantum numbersinanatom:(a)n53,l51;(b)n55,l53,ml 521; (c)n52,l51,ml 50;(d)n57?

[JChen_2I]

i believe this is how you do it:
a) 103 because ml can be any value between [-l, l] so there are 51*2+1 possible orbitals
bc) 1 because they give you a ml value so there's only one possible orbital
d) if n=57 then there are 57 possible l values and for each of them they'd have l*2+1 orbitals (or just l*2 if l=0)

[005321227]

i believe this is how you do it:
a) 103 because ml can be any value between [-l, l] so there are 51*2+1 possible orbitals
bc) 1 because they give you a ml value so there's only one possible orbital
d) if n=57 then there are 57 possible l values and for each of them they'd have l*2+1 orbitals (or just l*2 if l=0)

How come ml only has one possible orbital?

[JChen_2I]

i believe this is how you do it:
a) 103 because ml can be any value between [-l, l] so there are 51*2+1 possible orbitals
bc) 1 because they give you a ml value so there's only one possible orbital
d) if n=57 then there are 57 possible l values and for each of them they'd have l*2+1 orbitals (or just l*2 if l=0)

How come ml only has one possible orbital?

Because normally ml can be any value between [-l, l] which is why for a), we multiply the l value by 2 and add one for if ml=0. But bc) tell us that the ml value is 521 and 50 respectively so that is the only orbital possible.