The crystal field splitting energy for complex X is 3.34 x 10-19 J and complex Y is 3.78 x 10-19 J. What are the colors of these complexes? A. Complex X: Blue, Complex Y: Red B. Complex X: Violet, Complex Y: Orange C. Complex X: Blue, Complex Y: Yellow D. Complex X: Orange, Complex Y: Green
The crystal field splitting energy for complex X is 3.34 x 10-19 J and complex Y is 3.78 x 10-19 J. What are the colors of these complexes? A. Complex X: Blue, Complex Y: Red B. Complex X: Violet, Complex Y: Orange C. Complex X: Blue, Complex Y: Yellow D. Complex X: Orange, Complex Y: Green
Chemistry
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Chapter1: Chemical Foundations
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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![### Crystal Field Splitting and Coloration of Complexes
In this exercise, we are given the crystal field splitting energies for two complexes, X and Y. Their crystal field splitting energies (Δ) are as follows:
- Complex X: \( 3.34 \times 10^{-19} \) J
- Complex Y: \( 3.78 \times 10^{-19} \) J
The problem requires us to determine the colors of these complexes based on their crystal field splitting energies. The possible options are:
A. Complex X: Blue, Complex Y: Red
B. Complex X: Violet, Complex Y: Orange
C. Complex X: Blue, Complex Y: Yellow
D. Complex X: Orange, Complex Y: Green
#### Explanation
The color of a complex can be determined using the concept of crystal field theory. The observed color is complementary to the color absorbed due to the crystal field splitting of the d-orbitals.
1. **Determine the Absorbed Wavelength:**
The wavelength (λ) of light absorbed due to the crystal field splitting can be calculated using the energy equation:
\[
Δ = hν = \frac{hc}{λ}
\]
where:
- \( Δ \) is the crystal field splitting energy,
- \( h \) is Planck’s constant (\(6.626 \times 10^{-34} \) Js),
- \( c \) is the speed of light (\(3.00 \times 10^{8} \) m/s),
- \( ν \) is the frequency of light,
- \( λ \) is the wavelength of light.
2. **Find the Complementary Color:**
The color of the complex is the complementary color to the absorbed light. For instance, if a complex absorbs light in the red region, it will appear green.
Using the given options, we cross-reference the energy values with the known energy ranges for visible light absorption to determine the color of the complexes.
**Options:**
A. Complex X: Blue, Complex Y: Red
B. Complex X: Violet, Complex Y: Orange
C. Complex X: Blue, Complex Y: Yellow
D. Complex X: Orange, Complex Y: Green
### Conclusion
To solve this problem correctly, a detailed understanding of the relationship between crystal field splitting energy and the corresponding wavelengths/colors of absorbed light is essential.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5dfcff76-5646-42a0-b45c-1f5ea8195891%2Fa5a027db-07e1-4d88-a84c-c19d0ea6dc1a%2F2wn4ykne_processed.png&w=3840&q=75)
Transcribed Image Text:### Crystal Field Splitting and Coloration of Complexes
In this exercise, we are given the crystal field splitting energies for two complexes, X and Y. Their crystal field splitting energies (Δ) are as follows:
- Complex X: \( 3.34 \times 10^{-19} \) J
- Complex Y: \( 3.78 \times 10^{-19} \) J
The problem requires us to determine the colors of these complexes based on their crystal field splitting energies. The possible options are:
A. Complex X: Blue, Complex Y: Red
B. Complex X: Violet, Complex Y: Orange
C. Complex X: Blue, Complex Y: Yellow
D. Complex X: Orange, Complex Y: Green
#### Explanation
The color of a complex can be determined using the concept of crystal field theory. The observed color is complementary to the color absorbed due to the crystal field splitting of the d-orbitals.
1. **Determine the Absorbed Wavelength:**
The wavelength (λ) of light absorbed due to the crystal field splitting can be calculated using the energy equation:
\[
Δ = hν = \frac{hc}{λ}
\]
where:
- \( Δ \) is the crystal field splitting energy,
- \( h \) is Planck’s constant (\(6.626 \times 10^{-34} \) Js),
- \( c \) is the speed of light (\(3.00 \times 10^{8} \) m/s),
- \( ν \) is the frequency of light,
- \( λ \) is the wavelength of light.
2. **Find the Complementary Color:**
The color of the complex is the complementary color to the absorbed light. For instance, if a complex absorbs light in the red region, it will appear green.
Using the given options, we cross-reference the energy values with the known energy ranges for visible light absorption to determine the color of the complexes.
**Options:**
A. Complex X: Blue, Complex Y: Red
B. Complex X: Violet, Complex Y: Orange
C. Complex X: Blue, Complex Y: Yellow
D. Complex X: Orange, Complex Y: Green
### Conclusion
To solve this problem correctly, a detailed understanding of the relationship between crystal field splitting energy and the corresponding wavelengths/colors of absorbed light is essential.
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