(i) An atomic orbital has n = 3. What are the possible values of l and m_l?

(ii) List the quantum numbers (ml and l) of electrons for 3d orbital.

(iii) Which of the following orbitals are possible?

1p, 2s, 2p and 3f

(i) ‘n’ refers to the principle quantum number

‘l’ refers to the azimuthal quantum number

‘m’ refers to the magnetic quantum number

l can have any value from to n – 1.

So, for n= 3, the permissible value of l = 0, 1, 2

M can have any value from –l, -l+1 ………..0, 1 ……… l

For l = 0

m = 0

For l = 1

m = +1, 0, -1

For l = 2

m = +2, +1, 0, -1, -2

(ii) When l = 2 the value of m = -2, -1, 0, +1, +2

Now, for the 3d orbital:

Principal quantum number [n] = 3

Azimuthal quantum number [L] = 2

Magnetic quantum number [mL] = -2, -1, 0, 1, 2

(iii) For a given value of n the value of l can range from 0 to n-1
So for n =1, l = 0

Thus, 1p is not possible
For n = 2, l = 0 and 1

Therefore, 2s and 2p are possible orbitals.
For n = 3, l = 0, 1 and 2

So 3p is not possible.