2.2.1 The allowed values of quantum numbers Quantum Numbers m 010+1010+1Λ -2-10+1+2 -2-10+1+2 -3-2-10+1+2+3 Problem:What values of the azimuthal (1)and magnetic (m)quantum numbers are allowed for a principal quantum number(n)of 4?How many orbitals are allowed for n=4? Solution:The 1 values go from 0 to (n-1),and for n=3 they are: 1 =0,1,2,3.The values for m go from-1 to zero to +l For1=0,m1=0 1=1,m=-1,0,+1 1=2,m1=-2,-1,0,+1,+2 1=3,m1=-3,-2,-1,0,+1,+2,+3 There are 16 mr values,so there are 16 orbitals for n=4! The total number of orbitals for a given value of n is n2.Quantum Numbers n l ml 1 2 3 4 0 0 1 0 1 2 0 1 2 3 0 0 -1 0 +1 0 -1 0 +1 0 -1 0 +1 -2 -1 0 +1 +2 -2 -1 0 +1 +2 -3 -2 -1 0 +1 +2 +3 2.2.1 The allowed values of quantum numbers Problem: What values of the azimuthal (l) and magnetic (m) quantum numbers are allowed for a principal quantum number (n) of 4? How many orbitals are allowed for n=4? Solution: The l values go from 0 to (n-1), and for n=3 they are: l = 0,1,2,3. The values for m go from -l to zero to +l For l = 0, ml = 0 l = 1, ml = -1, 0, +1 l = 2, ml = -2, -1, 0, +1, +2 l = 3, ml = -3, -2, -1, 0, +1, +2, +3 There are 16 mL values, so there are 16 orbitals for n=4! • The total number of orbitals for a given value of n is n2