Problem 31 - Chemistry and Chemical Reactivity

Question

In water, the titanium(III) ion, \(\left[\mathrm{Ti}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+},\) has a broad absorption band centered at about \(500 \mathrm{nm}\). What color light is absorbed by the ion?

Step-by-Step Solution

Answer

The ion absorbs green light. The complementary color observed is red.

Step 1: Understanding Light Absorption

When a compound absorbs light, it removes a specific color from the visible spectrum. The color perceived is the complementary color of the absorbed light.

Step 2: Analyze the Wavelength

The ion \([\mathrm{Ti}(\mathrm{H}_{2}\mathrm{O})_{6}]^{3+}\) absorbs light at approximately \(500\, \mathrm{nm}\). This wavelength corresponds to green light in the visible spectrum.

Step 3: Determine the Complementary Color

To find the color observed, identify the complementary color to the absorbed wavelength. Green's complementary color in the color wheel is red.

Key Concepts

Color Perception

Color perception is how our eyes and brain interpret light with different wavelengths. When light strikes an object, the object can absorb some wavelengths and reflect others. The colors we see are the wavelengths of light that are not absorbed but reflected. For instance, if an object absorbs blue light, the color it appears will be the complement of blue on the color wheel, which is orange.

This concept is crucial in understanding chemical compounds like \( \left[\text{Ti}\left(\text{H}_2\text{O}\right)_6\right]^{3+} \), which absorbs light at specific wavelengths. As it absorbs green light, the visual perception will be its complementary color, red. This is why knowing the absorption wavelengths of compounds allows us to predict the color they will appear. A perfect synthesis of science and art, color perception plays a vital role in numerous fields like chemistry, design, and technology.

Visible Spectrum

The visible spectrum is a segment of the electromagnetic spectrum that the human eye can detect. It ranges from approximately 380 nm to 750 nm, covering all the colors we can see. Different colors correspond to different wavelengths within this range.

To identify colors in the visible spectrum:

• Violet encompasses around 380-450 nm.
• Blue ranges from 450-495 nm.
• Green spans 495-570 nm.
• Yellow is found between 570-590 nm.
• Orange occupies the 590-620 nm range.
• Red falls within 620-750 nm.

Understanding the visible spectrum helps us determine the color absorbed by a compound. For the titanium(III) ion absorbing at 500 nm, we confirm this falls into the green region. Thus, the complementary color, red, becomes visible to our perception. This knowledge is foundational in both the study of light in physics and practical applications in digital displays and lighting.

Wavelength

Wavelength is the distance between consecutive peaks of a wave and is typically measured in nanometers (nm) when dealing with light. Colors of light correspond to specific ranges of wavelengths in the visible spectrum.

Each color has a specific wavelength range, and the properties of different materials can affect which wavelengths are absorbed. The titanium(III) ion absorbs light primarily at a wavelength of 500 nm. Knowing the wavelength allows scientists to predict what color will be absorbed and which will be reflected or transmitted.

The equation to determine the energy of light based on wavelength is significant, represented by \[ E = \frac{hc}{\lambda} \]where \(E\) is energy, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength. This reveals how energy varies inversely with wavelength. In practice, understanding wavelengths enables applications in identifying chemical reactions and designing efficient optical instruments. It's all about lights and colors working together to help us see and understand the world.