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

(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

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(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 m0 = 0 m1 = –...
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(i) n = 3 (Given)

For a given value of n, l can have values from 0 to (n1).

∴ 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

m0 = 0

m1 = – 1, 0, 1

m2 = – 2, – 1, 0, 1, 2

(ii) For 3d orbital, l = 2.

For a given value of l, mlcan 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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