Problem 41 - Chemistry Matter and Change

Question

Rainbow What are two differences between the red and green electromagnetic waves in a rainbow?

Step-by-Step Solution

Answer

The two differences between red and green electromagnetic waves in a rainbow are: 1. Wavelength: Red light has a longer wavelength (approximately 700 nm) compared to green light (approximately 530 nm). 2. Frequency and Energy: Red light has a lower frequency (\(\sim 4.3 \times 10^{14}\) Hz) and lower energy, while green light has a higher frequency (\(\sim 5.6 \times 10^{14}\) Hz) and higher energy.

Step 1: Difference 1: Wavelength

The electromagnetic spectrum is divided into several regions, with visible light being one of them. Rainbow's colors represent the different wavelengths of visible light. Red light has a longer wavelength, typically around 700 nm, whereas green light has a shorter wavelength, approximately 530 nm. So the first difference between red and green light waves in a rainbow is their wavelength, with red light having a longer wavelength than green light.

Step 2: Difference 2: Frequency (and energy)

As we know, the frequency of a wave is inversely proportional to its wavelength. Since red and green electromagnetic waves have different wavelengths, they will also have different frequencies. Red light has a lower frequency (\(\sim 4.3 \times 10^{14}\) Hz) compared to green light (\(\sim 5.6 \times 10^{14}\) Hz). Along with frequency, the energy of the light waves is also different. A higher frequency corresponds to a higher energy, and a lower frequency corresponds to lower energy. Therefore, green light has more energy compared to red light.

Key Concepts

Wavelength of Light

Have you ever wondered why a rainbow has distinct colors? A key player in this spectacle is the wavelength of light. Light travels as a wave, and the distance between two consecutive peaks or troughs is what we call the wavelength. It's measured in nanometers (nm), with one nanometer being one billionth of a meter.

When it comes to a rainbow, red light has a longer wavelength, around 700 nm, and green light has a shorter wavelength, close to 530 nm. This difference in wavelength is why we see these colors at different positions in a rainbow. Shorter wavelengths bend more than longer ones when passing through water droplets, spreading out to display the spectrum of colors we love to see.

Frequency of Electromagnetic Waves

Closely related to the wavelength is the frequency of electromagnetic waves. The frequency tells us how many waves pass a given point per second and is measured in Hertz (Hz). As the wavelength gets shorter, the frequency gets higher because more waves can fit in the same space over a period of time.

Considering red and green light in a rainbow, the red light with its long 700 nm waves has a lower frequency, while green light with its shorter 530 nm waves is higher in frequency. This connection between frequency and wavelength helps us understand why different colors of light have different energies.

Visible Light Spectrum

The rainbow is a natural spectrum display, illustrating the visible light spectrum. This spectrum is just a small part of the vast electromagnetic spectrum which includes other types of waves like radio waves, ultraviolet light, and X-rays. However, the human eye can only detect light within a certain range of wavelengths, from approximately 380 nm to 750 nm. Within this band, each wavelength corresponds to a different color, from violet at the shortest end to red at the longest end. Therefore, when you're looking at a rainbow, you're actually viewing the visible light spectrum spread across the sky in a beautiful arc.

Energy of Light Waves

The energy of light waves is vitally important when it comes to understanding the physical world. Energy in a light wave is directly proportional to its frequency and inversely proportional to its wavelength. This means that waves with higher frequencies, and thus shorter wavelengths, carry more energy. In the context of a rainbow, even though green light has a shorter wavelength than red light, green light carries more energy because its frequency is higher. This is why ultraviolet light, which has an even shorter wavelength than visible light, can cause sunburn—it has enough energy to damage skin cells.