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Why is the outer structure of tungsten $\mathrm{5d^46s^2}$ instead of $\mathrm{5d^56s^1}$?

I try to explain this in comparison with outer structure of chromium $\mathrm{4d^55s^1}$ taking into consideration 5d orbitals have lesser energy than 6s orbitals in tungsten by saying that the size of the energy gap between the 3d and 4s orbitals lesser than size of the energy gap between the 5d and 6s orbitals, and the repulsion between electrons in the structure$\mathrm{5d^46s^2}$ more than the repulsion in the structure $\mathrm{5d^56s^1}$ which can push the electron from 5d to 6s to produce the lowest energy structure.

I need qualitative answer?

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Firstly note that the energetic differences between $\mathrm d^m\mathrm s^n$ and $\mathrm d^{m-1}\mathrm s^{n+1}$ configurations are generally not large. Sometimes these are not amenable to simple qualitative rationalisation.

However in this case it is possible to argue along two lines.

  1. Relativistic effects lead to the stabilisation of the 6s subshell and destabilisation of the 5d subshell, which directly favours population of 6s over 5d.

  2. Electron-electron repulsions in the 3d/4s orbitals are generally larger than repulsions in the 5d/6s orbitals, because the latter are more diffuse. Hence chromium chooses to adopt a configuration in which exchange energy is maximised (i.e. electron-electron repulsions are minimised).

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  • $\begingroup$ The energetic differences between 3d and 4s lesser or larger than energetic differences between 5d and 6s ? $\endgroup$
    – Adnan AL-Amleh
    Feb 23 '18 at 6:52
  • $\begingroup$ Electron-electron repulsions in the$\mathrm{5d^46s^2}$ structure are larger or lesser than repulsions in the $\mathrm{5d^56s^1}$ structure? $\endgroup$
    – Adnan AL-Amleh
    Feb 23 '18 at 7:13

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