2.28 (i) An atomic orbital has n = 3. What are the possible values of l and m?
(ii) List the quantum numbers (m and l ) of electrons for 3d orbital.
(iii) Which of the following orbitals are possible?
1p, 2s, 2p and 3f
(i) n = 3 (Given)
For a given value of n, l can have values from 0 to (n – 1).
For n = 3
l = 0, 1, 2
For a given value of l, ml can have (2l + 1) values.
For l = 0, m = 0 l = 1, m = – 1, 0, 1 l = 2, m = –
2, – 1, 0, 1, 2
For n = 3
l = 0, 1, 2
= 0
= – 1, 0, 1 m2 = –2, – 1, 0, 1, 2
(ii) For 3d orbital, l = 2.
For a given value of l, ml can have (2l + 1) values i.e., 5 values.
For l = 2 m2 = – 2, – 1, 0, 1, 2
(iii) Among the given orbitals only 2s and 2p are possible. 1p and 3f cannot exist.
For p-orbital, l = 1.
For a given value of n, l can have values from zero to (n – 1).
For l is equal to 1, the minimum value of n is 2.
Similarly,
For f-orbital, l = 4.
For l = 4, the minimum value of n is 5.
Hence, 1p and 3f do not exist.
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