Problem 21 - Basic Principles of Organic Chemistry

Question

What color would you expect to perceive if white light were passed through a solution containing a substance that absorbed very strongly but only within the specified wavelength ranges? a. \(660 \pm 30 \mathrm{~nm}\) b. \(530 \pm 30 \mathrm{~nm}\) c. \(^{*} 560 \pm 300 \mathrm{~nm}\) \(\mathbf{d} . * 480 \pm 0.1 \mathrm{~nm}\)

Step-by-Step Solution

Answer

a. Cyan. b. Magenta. c. Black. d. Yellow.

Step 1: Understand the Context

To solve this problem, we need to understand how light absorption works when passing through a substance. When certain wavelengths (colors) of white light are absorbed, the remaining light determines the perceived color.

Step 2: Light Absorption and Perceived Colors

White light consists of all visible wavelengths. When a substance absorbs light within a certain wavelength range, the absorbed color is removed from white light, and the complementary color is seen. We will evaluate each option to determine the expected perceived color.

Step 3: Analyze Absorption for Option a

Option a indicates absorption at wavelengths of around 660 nm, which corresponds to red light. By absorbing red light, the complementary color, cyan, is perceived.

Step 4: Analyze Absorption for Option b

Option b involves absorption at wavelengths around 530 nm, corresponding to green light. Therefore, the perceived color is magenta, the complementary color of green.

Step 5: Analyze Absorption for Option c

For option c, a wide range of wavelengths (260 nm to 860 nm) is absorbed, which covers almost all visible light. This would result in black or nearly no light being transmitted.

Step 6: Analyze Absorption for Option d

For option d, absorption occurs at 480 nm, corresponding to blue light. Thus, the complementary color, yellow, is expected to be the perceived color.

Key Concepts

Wavelength

Wavelength is one of the fundamental concepts in understanding how light behaves. It refers to the distance between two consecutive peaks of a wave and is measured in nanometers (nm) for light. When discussing visible light, different wavelengths correspond to different colors of light.

• Red light has longer wavelengths, approximately 620-750 nm.
• Green light has medium wavelengths, roughly 495-570 nm.
• Blue and violet lights have shorter wavelengths, around 450-495 nm and 380-450 nm, respectively.

Understanding wavelength is crucial when analyzing how substances absorb certain colors and, as a result, how other colors are perceived.

Complementary Colors

In color theory, complementary colors are pairs of colors that, when combined, cancel each other out by producing a grayscale color like white or black. However, in terms of light, when one color is absorbed, the complementary color becomes predominant in the spectrum we see. Examples of complementary color pairings include:

• Red and Cyan
• Green and Magenta
• Blue and Yellow

This is essential to understanding perceived colors in absorption. If a substance absorbs a specific wavelength, the complementary color will dominate the appearance of the material under white light.

Perceived Colors

Perceived colors are the result of the complex interaction between light and materials. When light hits an object, specific wavelengths can be absorbed, and the colors that aren't absorbed are reflected, which make up the color we perceive. For instance: - If red light is absorbed, cyan is the perceived color. - Absorption of green light results in the appearance of magenta. - Similarly, if blue light is absorbed, yellow becomes visible. Our brains process the combination of these reflected wavelengths to interpret them as specific colors. This perception is also influenced by factors such as context and surrounding colors.

Visible Spectrum

The visible spectrum refers to the portion of the electromagnetic spectrum that is visible to the human eye. It ranges from approximately 380 nm (violet) to 750 nm (red), covering the full spectrum of rainbow colors.

• The electromagnetic spectrum beyond violet is ultraviolet, which is not visible to humans but can be seen by some animals.
• Infrared, just beyond red, is also invisible to humans but some technology can detect it.

Understanding this spectrum is critical for comprehending why certain colors are absorbed and others are perceived. Every color we see is somewhere within this spectrum, and shifts in wavelength due to absorption lead to shifts in perceived color.