Question 57 of 62intermediate🔍 AnalyzeShort Answer3 marks

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. n = 4, l = 2, mₗ = –2, mₛ = –1/2
  2. n = 3, l = 2, mₗ = 1, mₛ = +1/2
  3. n = 4, l = 1, mₗ = 0, mₛ = +1/2
  4. n = 3, l = 2, mₗ = –2, mₛ = –1/2
  5. n = 3, l = 1, mₗ = –1, mₛ = +1/2
  6. n = 4, l = 1, mₗ = 0, mₛ = +1/2
Correct Answer

The order of increasing energies is: 5 < 2 = 4 < 3 = 6 < 1. Electrons 2 and 4 have the same energy, and electrons 3 and 6 have the same energy.

Exercise: EXERCISES | Q: 2.62 | (Page 41)
For More Understanding

Explanation

The principal quantum number (nn) determines the shell and to a large extent the energy, while the azimuthal quantum number (ll) determines the subshell and to some extent the energy in multi-electron atoms. By identifying the subshells for each electron, we can arrange them by their relative energies.

Solution Steps

  1. Step 1: Identify the subshell for each electron using nn and ll values (l=0l=0 is ss, l=1l=1 is pp, l=2l=2 is dd).

    1. n=4,l=2→4dn=4, l=2 \rightarrow 4d
    2. n=3,l=2→3dn=3, l=2 \rightarrow 3d
    3. n=4,l=1→4pn=4, l=1 \rightarrow 4p
    4. n=3,l=2→3dn=3, l=2 \rightarrow 3d
    5. n=3,l=1→3pn=3, l=1 \rightarrow 3p
    6. n=4,l=1→4pn=4, l=1 \rightarrow 4p

  2. Step 2: Arrange the subshells in order of increasing energy. Since nn determines energy to a large extent and ll to some extent, the energy order is 3p<3d<4p<4d3p < 3d < 4p < 4d.

  3. Step 3: Map the electrons to this energy order. The increasing order of energy is 5 < 2 = 4 < 3 = 6 < 1. Electrons 2 and 4 are in the same 3d3d subshell, so they have the same energy. Electrons 3 and 6 are in the same 4p4p subshell, so they have the same energy.

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