Final answer:
The color of a solution is the complementary color to the wavelength absorbed by the substance, which is determined by the λmax. The λmax can shift with changes in temperature, making objects appear bluer at higher temperatures due to the emission of shorter wavelengths.
Step-by-step explanation:
The relationship between the color of a solution and the color corresponding to the wavelength for λmax (lambda max) involves the interaction of light with the solution. When white light passes through or is reflected by a colored substance, certain wavelengths of light are absorbed, and the solution appears to be the complementary color to the wavelength absorbed. For example, if a substance absorbs light in the 420-430 nm range, it will appear yellow, the complementary color to the absorbed blue light. The observed color of a solution is determined by the λmax, which is the wavelength at which the maximum amount of light is absorbed; this wavelength corresponds to the substance's peak absorption in its absorption spectrum.
Furthermore, the color intensity and λmax can shift with changes in temperature, based on Wien's law, which states that a hotter object will have a λmax at a shorter wavelength and will therefore emit light of a bluer color. Metals glowing red at lower temperatures and turning white hot at higher temperatures exemplify this phenomenon, demonstrating the shift of λmax to shorter wavelengths as temperature increases.