Question
The quantum numbers of six electrons are given below. Arrange them in order of increasing energies. If any of these combination(s) has/ have the same energy lists:
  1. $\text{n}=4,\text{l}=2,\text{m}_\text{l}=-2,\text{m}_{\text{s}}=-\frac{1}{2}$
  2. $\text{n}=3,\text{l}=2,\text{m}_\text{l}=1,\text{m}_{\text{s}}=+\frac{1}{2}$
  3. $\text{n}=4,\text{l}=1,\text{m}_\text{l}=0,\text{m}_{\text{s}}=+\frac{1}{2}$
  4. $\text{n}=3,\text{l}=2,\text{m}_\text{l}=-2,\text{m}_{\text{s}}=-\frac{1}{2}$
  5. $\text{n}=3,\text{l}=1,\text{m}_\text{l}=-1,\text{m}_{\text{s}}=+\frac{1}{2}$
  6. $\text{n}=4,\text{l}=1,\text{m}_\text{l}=0,\text{m}_{\text{s}}=+\frac{1}{2}$

Answer

For n = 4 and l = 2, the orbital occupied is 4d.
For n = 3 and l = 2, the orbital occupied is 3d.
For n = 4 and l = 1, the orbital occupied is 4p.
Hence, the six electrons i.e., 1, 2, 3, 4, 5, and 6 are present in the 4d, 3d, 4p, 3d, 3p, and 4p orbitals respectively.
Therefore, the increasing order of energies is 5(3p) < 2(3d) = 4(3d) < 3(4p) = 6(4p) < 1(4d).

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