Question

how many hydrogen orbitals exist with the same n=3 value but with different l and m values?

Answer 1

Since l varies from 0 to n-1, for n=3 l is equal to 0, 1, 2

m varies from -l to +l

Thus, m is equal to -2, -1, 0, 1, or 2 for l=2

m is equal to -1,0,1 for l=1

m is equal to 0 for l=0

So, there are 9 hydrogen orbitals with n=3 and with different values of l and m