Question

Which of the following colors in the visible part of the spectrum has the lowest energy? (A) red light (B) green light (C) purple light (D) blue light

Short answer

The energy of light is inversely proportional to its wavelength. Among the given options, red light has the longest wavelength, which means it has the lowest energy. Therefore, the correct answer is (A) red light.

Step-by-step solution

List the relationships between energy, frequency, and wavelength.

We know that the energy of light is given by the formula E = h * f and the frequency is related to wavelength by the formula f = c / λ, which leads to E = h * c / λ.

Determine the relationship between energy and wavelength.

From the equation E = h * c / λ, we can determine that energy is inversely proportional to the wavelength. So, a shorter wavelength corresponds to higher energy, and a longer wavelength corresponds to lower energy.

Analyze the given options.

We are given four options of different colors in the visible spectrum: red, green, purple, and blue. It is known that red light has the longest wavelength, followed by green, blue, and purple light.

Determine the color with the lowest energy.

Since energy is inversely proportional to wavelength and red light has the longest wavelength, we can conclude that red light has the lowest energy among the given options. Hence, the correct answer is (A) red light.

Key concepts

Energy and Wavelength Relationship

Light, as we see it, has both energy and wavelength. These two properties are closely linked. The energy of a light wave can be described using the equation \(E = h \cdot f\), where \(E\) is energy, \(h\) is Planck's constant, and \(f\) is frequency. But there's more to it because frequency \(f\) itself is related to wavelength by the formula \(f = \frac{c}{\lambda}\), where \(c\) is the speed of light and \(\lambda\) is the wavelength.

Combining these, we get \(E = \frac{h \cdot c}{\lambda}\). This means that energy \(E\) is inversely proportional to wavelength \(\lambda\).

• If the wavelength is longer, energy is lower.
• If the wavelength is shorter, energy is higher.

This indicates that the shorter the wavelength, the more energy the light wave carries. Understanding this relationship is key to determining which colors in the visible spectrum have more or less energy.

Color Energy Comparison

When we talk about color, we refer to the visible part of the electromagnetic spectrum that our eyes can detect. Each color corresponds to a particular range of wavelengths, and therefore, energies.

• Red light has the longest wavelength and, consequently, the lowest energy.
• Green light has a shorter wavelength and more energy compared to red.
• Blue and purple light have the shortest wavelengths in the visible spectrum, which gives them the highest energy levels among these four options.

This difference in energy becomes crucial in applications like lasers or fiber optics, where specific colors/wavelengths might be chosen based on the energy requirements of the process involved. The lower energy in red light's longer wavelength makes it less energetic, which can be pivotal in determining its applications.

Light Wavelength

The wavelength of light tells us how long the wave stretches in space, measured usually in nanometers (nm). Each color in the visible light spectrum corresponds to a particular range of these wavelengths.

In the visible spectrum:

• Red light typically falls in the range between 620-750 nm, which makes it the longest in the visible spectrum.
• Green light lies between 495-570 nm, offering a balance with its moderate wavelength.
• Blue light spans from 450-495 nm, and even shorter than blue lies purple light at about 380-450 nm.

The spectrum shows a seamless transition of wavelengths from one color to another. The variations in these wavelengths dictate the energy and ultimately how we perceive different colors. Recognizing this can help us understand why certain technologies utilize specific colors; for example, why some therapies might use blue light for its higher energy to achieve better results.