1. How many lvalues are associated with n = 3 ? (b) How many${\mathbf{m}}_{\mathbf{l}}$values are associated with l =1 ?

The given quantum numbers are:

1. The principal quantum number, n = 3
2. The orbital quantum number, l = 1

For every given value of principal quantum number , there exist values of orbital quantum number l, ranging from 0 to (n -1) . Similarly, for every given value of orbital quantum number l , there exists -l to +l values for each magnetic quantum number, ${\mathbf{m}}_{\mathbf{l}}$.

For n = 3 the orbital quantum number is,

l = 0,1,2

Thus, in n = 3 , number of subshells l = 3 .

Using the concept, there are 3 l values ranging from 0 to 2 associated with n = 3.

Hence, there are 3 values.

For l = 3 the magnetic quantum number is,

${\mathrm{m}}_{\mathrm{l}}=-1,0,1$ for l = 0 ; total ${\mathrm{m}}_{\mathrm{l}}$ value is 3 .

Using the concept, there are 3 values of ${\mathrm{m}}_{\mathrm{l}}$ ranging from -1 to +1 associated with l = 1

Hence, there are 3${\mathrm{m}}_{\mathrm{l}}$ values.