Textbook Question
The lobes of which d orbitals point directly between the ligands in a. octahedral geometry,
Ch.23 - Transition Metals and Coordination Chemistry
Chapter 23, Problem 47
Complete the exercises below. a. If a complex absorbs light at 610 nm, what color would you expect the complex to be? b. What is the energy in joules of a photon with a wavelength of 610 nm? c. What is the energy of this absorption in kJ/mol?
Verified step by step guidance1
Step 1: To determine the color of the complex, first understand that the color observed is complementary to the color absorbed. Use the color wheel to find the complementary color of 610 nm, which is in the orange-red region.
Step 2: To find the energy of a photon with a wavelength of 610 nm, use the equation E = \frac{hc}{\lambda}, where h is Planck's constant (6.626 \times 10^{-34} \text{ J s}), c is the speed of light (3.00 \times 10^8 \text{ m/s}), and \lambda is the wavelength in meters.
Step 3: Convert the wavelength from nanometers to meters by using the conversion factor 1 nm = 1 \times 10^{-9} m.
Step 4: Calculate the energy of one photon in joules using the values from Step 2 and the converted wavelength from Step 3.
Step 5: To find the energy in kJ/mol, multiply the energy of one photon by Avogadro's number (6.022 \times 10^{23} \text{ mol}^{-1}) and convert the result from joules to kilojoules by dividing by 1000.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Color Absorption and Complementary Colors
When a complex absorbs light at a specific wavelength, it appears to be the complementary color of that wavelength. For example, if a complex absorbs light at 610 nm, which corresponds to orange light, it would appear blue-green, the complementary color on the color wheel. Understanding this relationship helps predict the visible color of substances based on their absorption spectra.
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Photon Energy and Wavelength Relationship
The energy of a photon is inversely related to its wavelength, described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. This relationship indicates that shorter wavelengths correspond to higher energy photons. For a wavelength of 610 nm, this equation can be used to calculate the energy in joules.
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Energy Conversion to kJ/mol
To convert the energy of a single photon to energy per mole, we use Avogadro's number (approximately 6.022 x 10²³ mol⁻¹). The energy in joules for one photon can be multiplied by Avogadro's number to find the energy in kJ/mol. This conversion is essential in chemistry for relating microscopic phenomena to macroscopic quantities relevant in reactions and processes.
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