Question

Identify the form of electromagnetic radiation in each pair that has the greater energy: a. green light or yellow light b. microwaves or blue light

Short answer

a. Green light has greater energy.b. Blue light has greater energy.

Step-by-step solution

Understand the Relationship Between Wavelength and Energy

Electromagnetic radiation energy is inversely proportional to its wavelength. This means shorter wavelengths have higher energy and longer wavelengths have lower energy. The equation that describes this relationship is \(E = \frac{hc}{\text{wavelength}}\), where \(E\) is energy, \(h\) is Planck's constant, and \(c\) is the speed of light.

Identify the Wavelengths of Green Light and Yellow Light

Green light has wavelengths roughly in the range of 495-570 nm, while yellow light has wavelengths around 570-590 nm. Since green light has a shorter wavelength than yellow light, green light has more energy.

Identify the Wavelengths of Microwaves and Blue Light

Microwaves have wavelengths ranging from 1 millimeter (mm) to 1 meter (m), whereas blue light has wavelengths ranging from about 450-495 nm. Blue light has a much shorter wavelength compared to microwaves, so blue light has more energy.

Compare Energies Based on Wavelengths

Based on the inverse relationship between wavelength and energy, and the wavelengths provided: (a) Between green light and yellow light, green light has greater energy.(b) Between microwaves and blue light, blue light has greater energy.

Key concepts

wavelength

Wavelength is a fundamental concept in understanding electromagnetic radiation. It is the distance between successive peaks of a wave. Different colors of light have different wavelengths. For instance, green light has a wavelength range of about 495-570 nm, while yellow light ranges from 570-590 nm.

Shorter wavelengths mean higher energy. This principle is critical in determining which electromagnetic wave has more energy. You can remember that as wavelength decreases, energy increases. This concept helps us explain why green light (with a shorter wavelength) has more energy than yellow light.

energy

Energy of electromagnetic radiation is closely tied to its wavelength. The relationship between energy (\(E\)) and wavelength (\text{wavelength})) is given by the equation: equation)equation). This equation reveals that energy is inversely proportional to wavelength. Thus, shorter wavelengths correspond to higher energy.

When comparing different forms of electromagnetic radiation, this relationship helps us determine which has greater energy. For instance, blue light has a much shorter wavelength than microwaves, meaning blue light has significantly higher energy.

electromagnetic spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, sorted by wavelength. It ranges from radio waves with the longest wavelengths to gamma rays with the shortest. Colors of visible light, like green and yellow, are just a small part of this spectrum.

Understanding the electromagnetic spectrum helps in recognizing the various forms of radiation and their characteristics. For example, microwaves have much longer wavelengths compared to visible light and consequently have lower energy. Knowing where different types of radiation fall on the spectrum allows us to predict their energy levels and behavior.

Planck's constant

Planck’s constant (\(h\)) is a pivotal value in quantum physics that links the energy of a photon to its frequency. The value of Planck's constant is approximately 6.63 x 10\(^{-34}\) Js. This constant is essential in the equation equation), which connects energy and wavelength.

Using Planck’s constant, we can calculate the energy for specific wavelengths of light. For example, when given the wavelength of green light, we can use Planck’s constant to determine its precise energy, reaffirming that green light has more energy than yellow light with a longer wavelength.