The correct order of the wavelength maxima of the absorption band in the ultraviolet-visible region

Q: Why does the oxidation state of Cobalt matter here?

The oxidation state affects the magnitude of crystal field splitting ($\Delta_o$). Higher oxidation states generally lead to larger splitting. Since all complexes here have $Co^{3+}$, we only need to compare the ligands.

Q: Do I need to memorize the entire spectrochemical series?

While you don't need to memorize every single ligand, knowing the relative order of common ligands (like Halides < Oxygen donors < Nitrogen donors < Carbon donors) is crucial for JEE.

Q: Why is wavelength inversely proportional to splitting energy?

According to Planck's equation, $E = \frac{hc}{\lambda}$. The energy required for the d-d transition equals the splitting energy $\Delta_o$. Thus, $\Delta_o = \frac{hc}{\lambda}$, making them inversely proportional.

Q: What if a complex has mixed ligands, like $[Co(NH_3)_5(Cl)]^{2+}$?

For mixed ligands, the overall field strength is roughly an average of the individual ligands' strengths. Since $Cl^-$ is much weaker than $NH_3$, replacing one $NH_3$ with $Cl^-$ decreases the overall $\Delta_o$ compared to $[Co(NH_3)_6]^{3+}$.

Q: Does the absorbed wavelength determine the color of the complex?

Yes, but indirectly! The complex absorbs a specific wavelength (color) from white light, and the color we observe is the complementary color (the remaining light that is transmitted or reflected).

Question

The correct order of the wavelength maxima of the absorption band in the ultraviolet-visible region for the given complexes is

Options:

(A) $[Co(CN)_6]^{3-} < [Co(NH_3)_6]^{3+} < [Co(NH_3)_5(H_2O)]^{3+} < [Co(NH_3)_5(Cl)]^{2+}$

(B) $[Co(NH_3)_5(Cl)]^{2+} < [Co(NH_3)_5(H_2O)]^{3+} < [Co(NH_3)_6]^{3+} < [Co(CN)_6]^{3-}$

(C) $[Co(CN)_6]^{3-} < [Co(NH_3)_5(Cl)]^{2+} < [Co(NH_3)_5(H_2O)]^{3+} < [Co(NH_3)_6]^{3+}$

(D) $[Co(NH_3)_6]^{3+} < [Co(CN)_6]^{3-} < [Co(NH_3)_5(Cl)]^{2+} < [Co(NH_3)_5(H_2O)]^{3+}$

Sigma Percentile · Accepted Answer

### The Colorful World of Coordination Compounds

Have you ever wondered why transition metal complexes exhibit such brilliant and diverse colors? The secret lies deep within their electronic structure, specifically in how their d-orbitals interact with surrounding molecules called ligands.

In this problem, we are tasked with arranging four different Cobalt(III) complexes in order of their absorption wavelength maxima. Let's embark on a journey through Crystal Field Theory to decode this!

### The Crystal Field Splitting

Imagine a central metal ion, like $Co^{3+}$, sitting in isolation. Its five d-orbitals are perfectly degenerate, meaning they all have the exact same energy.

However, when ligands approach this metal ion to form an octahedral complex, they bring their own electron clouds. The repulsion between the ligand electrons and the metal's d-electrons causes these five orbitals to split into two distinct energy levels: a lower energy set called $t_{2g}$ and a higher energy set called $e_g$.

The energy difference between these two levels is known as the **Crystal Field Splitting Energy**, denoted by $\Delta_o$.

### The Energy-Wavelength Connection

When white light shines on the complex, an electron in the lower $t_{2g}$ level can absorb a photon and jump to the higher $e_g$ level.

The energy of this absorbed photon must exactly match the energy gap, $\Delta_o$. According to Planck's equation, the energy of a photon is inversely proportional to its wavelength:

$$E = \frac{hc}{\lambda} = \Delta_o$$

This inverse relationship is the master key to our problem: **a larger splitting energy ($\Delta_o$) means a shorter absorbed wavelength ($\lambda$), and vice versa.**

### The Spectrochemical Series

Now, let's look at our specific complexes. The central metal ion is always $Co^{3+}$, so the only variable is the type of ligand attached. We have four ligands to compare: $Cl^-$, $H_2O$, $NH_3$, and $CN^-$.

How do we know which ligand causes a larger split? We use the **Spectrochemical Series**, an experimentally derived list that ranks ligands based on their field strength.

According to the series, the order of field strength is:

$$Cl^- < H_2O < NH_3 < CN^-$$

Here, $Cl^-$ is a weak field ligand, causing a small energy gap, while $CN^-$ is a strong field ligand, causing a massive energy gap.

### The Final Calculation

Since the splitting energy $\Delta_o$ follows the ligand strength:

$$\Delta_o(Cl^-) < \Delta_o(H_2O) < \Delta_o(NH_3) < \Delta_o(CN^-)$$

We simply invert this order to find the sequence of absorbed wavelengths:

$$\lambda(CN^-) < \lambda(NH_3) < \lambda(H_2O) < \lambda(Cl^-)$$

Translating this back to our given complexes, the correct order is:

$$[Co(CN)_6]^{3-} < [Co(NH_3)_6]^{3+} < [Co(NH_3)_5(H_2O)]^{3+} < [Co(NH_3)_5(Cl)]^{2+}$$

This perfectly matches Option (A).

The next time you see a brightly colored chemical solution, remember the elegant quantum dance of d-electrons and ligands happening right before your eyes!

Animated Solution for Chemistry - Coordination Compounds: The correct order of the wavelength maxima of the absorption band in the ultraviolet-visible region for the given complexes is

Select Answer:

Visualized Solution

\text{Crystal Field Splitting}

\text{Energy and Wavelength Relation}

\text{Identifying the Ligands}

\text{Spectrochemical Series}

\text{Order of } \Delta_o

\text{Final Wavelength Order}

\text{Color and Absorption}

The Sigma Insight: Bonding and Crystal field

The Colorful World of Coordination Compounds

The Crystal Field Splitting

The Energy-Wavelength Connection

The Spectrochemical Series

The Final Calculation

Similar Questions

The correct order of intensity of colors of the compound is

Arrange the following cobalt complexes in the order of increasing crystal field stabilisation energy (CFSE) value. $[C o F_{6}]^{3 -} (A), [C o (H_{2} O)_{6}]^{3 +} (B), [C o (N H_{3})_{6}]^{3 +} (C) and [C o (e n)_{3}]^{3 +} (D)$ Choose the correct option.

Which one of the following metal complexes is most stable?

The octahedral complex of a metal ion $M^{3 +}$ with four monodentate ligands $L_{1}, L_{2}, L_{3}$ and $L_{4}$ absorb wavelengths in the region of red, green, yellow and blue, respectively. The increasing order of ligand strength of the four ligands is

Homoleptic octahedral complexes of a metal ion $M^{3 +}$ with three monodentate ligands $L_{1}, L_{2}$ and $L_{3}$ absorb wavelengths in the region of green, blue and red respectively. The increasing order of the ligand strength is

Two complexes $[C r (H_{2} O)_{6}] C l_{3}$ (A) and $[C r (N H_{3})_{6}] C l_{3}$ (B) are violet and yellow coloured, respectively. The incorrect statement regarding them is

In which of the following order the given complex ions are arranged correctly with respect to their decreasing spin only magnetic moment? (i) $[F e F_{6}]^{3 -}$ (ii) $[C o (N H_{3})_{6}]^{3 +}$ (iii) $[N i C l_{4}]^{2 -}$ (iv) $[C u (N H_{3})_{4}]^{2 +}$

Among the ligands $NH_{3}$ , $en$ , $CN^{-}$ and $CO$ , the correct order of their increasing field strength, is