A solution of a complex ion absorbs visible light at a...

A solution of a complex ion absorbs visible light at a wavelength of $540 \mathrm{~nm}$.
(a) What is the color of the solution?
(b) Calculate the energy of an absorbed photon in joules and in $\mathrm{kJ} / \mathrm{mol}$.

Key Concepts

Electronic Transitions in Complex Ions

Complex ions, particularly those involving transition metals, absorb visible light as a result of electronic transitions between d-orbitals. These d–d transitions are responsible for the characteristic colors of coordination compounds, as they involve the promotion of electrons between energy levels that are split by the ligand field.

Molar Energy Conversion

Once the energy per photon is determined, it can be converted into an energy per mole value by multiplying by Avogadro's number. This conversion bridges the gap between microscopic particle energy and macroscopic quantities encountered in chemical reactions, making it easier to relate photon energy to chemical processes occurring on a molar scale.

Color Complementarity

When a solution absorbs light of a specific wavelength, the color observed is typically the complementary color of the absorbed light. This concept, rooted in color theory, explains that the perceived color arises from the wavelengths that are transmitted or reflected rather than those absorbed, which is particularly relevant in understanding the appearance of complex ion solutions in coordination chemistry.

Photon Energy Calculation

The energy of a photon is calculated using Planck’s equation, E = hc/?, where h is Planck’s constant, c is the speed of light, and ? is the wavelength of the absorbed light. This fundamental principle in quantum mechanics relates the energy of light to its wavelength, enabling the calculation of discrete energy values associated with electromagnetic radiation.

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