The Question is from neet-chemistry coordination-compounds crystal-field-theory, and it was created by the author THIRUPATHI REDDY

Question

A tetrahedral complex absorbs light of frequency $
u_1$ while a square planar complex of the same metal and ligands absorbs light of frequency $
u_2$.  If crystal field splitting in the tetrahedral complex is $\Delta_t$ and in the square planar complex is $\Delta_{sp}$, assuming $\Delta_{sp} = \frac{4}{9}\Delta_o$ and $\Delta_t = \frac{4}{9}\Delta_o$, which relationship between $
u_1$ and $
u_2$ is most likely?

THIRUPATHI REDDY · Accepted Answer

## CORE INFORMATION\n✓ **Answer**: A\n## CONCEPT FRAMEWORK\n\t**Primary Concept**: Crystal Field Theory and Spectrochemical Series\n\t**Related Topics**: Ligand Field Theory, d-orbital splitting, relationship between energy, frequency, and wavelength\n\t**Prerequisites**: Understanding of crystal field splitting in different geometries (tetrahedral and square planar), and the relationship between the energy of absorbed light and the crystal field splitting parameter.\n## SOLUTION PATHWAY\n**Given Information**:\n\t*   Tetrahedral complex absorbs light with frequency $\nu_1$ and crystal field splitting $\Delta_t$.\n\t*   Square planar complex absorbs light with frequency $\nu_2$ and crystal field splitting $\Delta_{sp}$.\n\t*   $\Delta_{sp} = \frac{4}{9}\Delta_o$\n\t*   $\Delta_t = \frac{4}{9}\Delta_o$\n**Method & Steps**:\n\t1. Relate the energy of absorbed light to the crystal field splitting.\n\t\tReasoning: The energy of absorbed light is directly proportional to the crystal field splitting parameter ($\Delta$). The frequency of light is also directly proportional to the energy.\n\t\tFormula/Rule: E = h$\nu$ and E = \Delta, therefore, \Delta \propto \nu\n\t2. Compare the crystal field splitting values for the two complexes.\n\t\tWorking: Given $\Delta_{sp} = \frac{4}{9}\Delta_o$ and $\Delta_t = \frac{4}{9}\Delta_o$, we have $\Delta_{sp} = \Delta_t$.\n\t\tKey Point: Since the crystal field splitting parameters are equal, the energy of the absorbed light will also be the same.\n\t3. Relate the frequencies of light absorbed by the two complexes.\n\t\tResult: Since the energy of the absorbed light is the same for both complexes, their frequencies will also be the same, i.e. $\nu_1 = \nu_2$.\n\t\tVerification: The equality of the crystal field splitting values directly implies the equality of the frequencies of absorbed light.\n## OPTION ANALYSIS\n[A] ✓: The crystal field splitting in both the tetrahedral and square planar complexes is given as $\frac{4}{9}\Delta_o$. Since the energy of absorbed light is directly proportional to the crystal field splitting, and frequency is directly proportional to energy, the frequencies are equal. Hence, $\nu_1 = \nu_2$.\n[B] :x: This option implies that the frequency absorbed by the tetrahedral complex is twice that of the square planar complex. This is incorrect because their crystal field splitting values are equal.\n[C] :x: This option implies that the frequency absorbed by the tetrahedral complex is half that of the square planar complex. This is incorrect because their crystal field splitting values are equal.\n[D] :x: This option implies that the frequency absorbed by the tetrahedral complex is four times that of the square planar complex. This is incorrect because their crystal field splitting values are equal.\n## LEARNING AIDS\n\t**Common Mistakes**:\n\t\t1.[Error 1]: Incorrectly assuming that tetrahedral and square planar complexes always have different splitting energies. In this case, they are given to be the same.\n\t\t2.[Error 2]: Not relating the crystal field splitting to the energy and frequency of the absorbed light directly. E = h$\nu$ and E = \Delta, therefore, \Delta \propto \nu\n\t**Quick Tips**:\n\t\t1.[Helpful shortcut]: If the crystal field splitting values are equal, then the frequencies of absorbed light will also be equal.\n\t\t2.[Memory aid]: Remember that higher crystal field splitting results in higher energy light absorption, which also means higher frequency and shorter wavelength.

THIRUPATHI REDDY · Answer

The correct Option is "$
u_1 = 
u_2$"

THIRUPATHI REDDY · Answer

$
u_1 = 2
u_2$

THIRUPATHI REDDY · Answer

$
u_1 = \frac{1}{2}
u_2$

THIRUPATHI REDDY · Answer

$
u_1 = 4
u_2$

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