How many orbitals are described by each of the below combinations of quantum numbers? n = 3, ℓ =2 orbitals n = 4, ℓ = 2, mℓ = 2 orbitals

Answer 1

Quantum numbers (n,l,ml, ms)

n=3. refers to 3rd energy level 3rd energy level has 3 possible values of l d has 5 different orientations

s=0. p=1. d=2 -2,-1,0,1,2

answer- n=3 l=2. number of orbitals-5

n=4 refers to 4th energy level 4th level has 4 possible l values Repeat from above for d

s=0 p=1 d=2 f=3

n=4 l=2. ml=2

answer- The number of orbitals is 5 and the ml=2 is referring to the last(5th) orbital space 4d

Answer 2

n = 3, l = 2 describes 5 orbitals since l = 2 denotes d orbitals and there are 5 of them.

n = 4, l = 2, ml = 2 describes 1 orbital since l = 2 denotes d orbitals, of which there are 5, but the ml = 2 defines the particular d orbital in question