Chapter 26: Problem 5

Discuss the splitting pattern of following energy terms under the effect of weak \(\mathrm{V}_{\text {oct }}\) and \(\mathrm{V}_{\text {tet. }}\) (a) \({ }^{3} \mathrm{P}\) (b) \({ }^{5} D\) (c) \({ }^{4} F\) (d) \({ }^{6} 5\)

Short Answer

Expert verified

^3P term under the effect of weak \(\mathrm{V}_{\text {oct }}\) and \(\mathrm{V}_{\text {tet }}\) splits into ^3T1g and ^3T2g; and ^3A2 and ^3T2 energy states respectively. ^5D term splits into ^5D, ^5Eg, and ^5T2g; and ^5E and ^5T2 energy states in weak \(\mathrm{V}_{\text {oct }}\) and \(\mathrm{V}_{\text {tet }}\) respectively. ^4F term leads to energy states of ^4A2g, ^4Eg, and ^4T1g; and ^4A2, ^4E, and ^4T2 energy states in \(\mathrm{V}_{\text {oct }}\) and \(\mathrm{V}_{\text {tet }}\) respectively. The last term looks like a typo and needs to be corrected.

Step by step solution

- Analyzing the ^3P term

The term symbol ^3P denotes an atom/molecule with two unpaired electrons in different orbits. In an octahedral field (weak), it splits into ^3T1g and ^3T2g energy states. Under a tetrahedral field, ^3P splits into ^3A2 and ^3T2 energy states.

- Analyzing the ^5D term

The term symbol ^5D denotes an atom/molecule with four unpaired electrons. In a weak octahedral field, this term splits into ^5D, ^5Eg, and ^5T2g energy states. Under a tetrahedral field, ^5D splits into ^5E and ^5T2 energy states.

- Analyzing the ^4F term

The term symbol ^4F represents an atom/molecule with three unpaired electrons. In a weak octahedral field, this term leads to energy states of ^4A2g, ^4Eg, and ^4T1g. In a tetrahedral field, ^4F splits into ^4A2, ^4E, and ^4T2 energy states.

- Analyzing the ^65 term

This looks like a typo in the problem, because representations in term symbols usually combine a superscript indicating the spin multiplicity with a capital letter indicating the orbital angular momentum (S, P, D, F,...), and not a number such as 5. Please correct it to get a valid term symbol.

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Discuss the splitting pattern of following energy terms under the effect of weak \(\mathrm{V}_{\text {oct }}\) and \(\mathrm{V}_{\text {tet. }}\) (a) \({ }^{3} \mathrm{P}\) (b) \({ }^{5} D\) (c) \({ }^{4} F\) (d) \({ }^{6} 5\)

Short Answer

Step by step solution

- Analyzing the ^3P term

- Analyzing the ^5D term

- Analyzing the ^4F term

- Analyzing the ^65 term

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