Problem 2 - Chemistry and Chemical Reactivity

Question

Consider the colors of the visible spectrum. (a) Which colors of light involve less energy than green light? (b) Which color of light has photons of greater energy, yellow or blue? (c) Which color of light has the higher frequency, blue or green?

Step-by-Step Solution

Answer

(a) Red, orange, and yellow. (b) Blue. (c) Blue.

Step 1: Understanding Energy and Wavelength

The visible spectrum consists of colors ordered by their wavelength, from longest to shortest: red, orange, yellow, green, blue, indigo, and violet. Energy is inversely related to wavelength, meaning colors with longer wavelengths have less energy.

Step 2: Identifying Colors with Less Energy than Green

Green light has a wavelength around 495-570 nm. Colors with longer wavelengths than green in the visible spectrum (red, orange, yellow) have less energy than green light.

Step 3: Comparing Energy of Yellow and Blue Photons

Yellow light has a wavelength around 570-590 nm, while blue light has a wavelength around 450-495 nm. Since blue light has a shorter wavelength, it has more energy than yellow light.

Step 4: Comparing Frequency of Blue and Green Light

Frequency is directly related to energy and inversely related to wavelength. Since blue light has a shorter wavelength and more energy than green light, it also has a higher frequency.

Key Concepts

Wavelength and Energy Relationship

In the visible spectrum, the wavelength of light plays a crucial role in determining the energy of the light. This relationship is inversely proportional, meaning that as the wavelength decreases, the energy increases, and vice versa.
For instance:

• Light with longer wavelengths, like red and orange, have lesser energy compared to shorter wavelengths, like blue and violet.
• The order of colors from longest to shortest wavelength is: red, orange, yellow, green, blue, indigo, violet.

By understanding this relationship, you can predict which colors of light will have more or less energy based solely on their wavelengths. For example, any color with a wavelength longer than that of green light will possess less energy. That's why red, orange, and yellow are lower in energy compared to green.

Frequency of Light

The frequency of light is directly related to its energy and inversely related to its wavelength. Light frequency refers to how many cycles of a wave pass a point in one second. The higher the frequency, the more energy the light has.
Consider these points:

• High-frequency light (like blue and violet) has high energy and shorter wavelengths.
• Low-frequency light (such as red and orange) has lower energy and longer wavelengths.

An example of light frequency in action is comparing green and blue light. Since blue light has a shorter wavelength than green, it possesses a higher frequency and thus, more energy.

Photon Energy

Photon energy is a handy concept for understanding light energy at the quantum level. Each photon, which is a packet of light, has energy determined by its frequency, according to the formula: \[ E = h \cdot f \]where \( E \) is the photon's energy, \( h \) is Planck's constant, and \( f \) is the frequency of the light. This means:

• Light with higher frequency (like blue) has photons with more energy compared to light with lower frequency (like yellow).
• A photon from blue light will have more energy than one from yellow light due to its higher frequency.

Understanding photon energy allows us to compare different colors of light, helping us answer questions like whether blue or yellow light has more energetic photons.

Visible Light Colors

Visible light encompasses all the colors that can be seen by the human eye. These colors form a spectrum from red to violet, each with distinct wavelengths and energies. Some important aspects to consider are:

• Red light has the longest wavelength and lowest energy, while violet has the shortest wavelength and highest energy.
• Colors you see everyday, like blue or yellow, each have unique wavelengths and energies.

This variety in the visible spectrum explains why different colors are used for diverse purposes in everyday technology and nature. For instance, blue light's high energy makes it significant in electronic displays, while the soothing nature of green is often utilized for restful visuals.