Question

Examine each of the following pairs and state which of the two has the higher energy: (a) microwaves and infrared, (b) visible light and infrared, (c) ultraviolet light and \(\mathrm{X}\) rays, (d) visible light and ultraviolet light.

Short answer

The type of electromagnetic radiation with higher energy for each pair is: (a) infrared, (b) visible light, (c) \text{X} rays, (d) ultraviolet light.

Step-by-step solution

- Understanding the Electromagnetic Spectrum

The electromagnetic spectrum is the range of all types of electromagnetic radiation. Radiation is energy that travels and spreads out as it goes. The different types of radiation are defined by their wavelengths and frequencies. Higher frequency corresponds to higher energy.

- Compare Wavelengths and Frequencies for Each Pair

Wavelength and frequency are inversely related; as the frequency of the wave increases, its wavelength decreases. Energy of a photon is directly proportional to its frequency; so, higher frequency means higher energy, and consequently, shorter wavelength also means higher energy.

- Analyzing Each Pair Individually

Based on the frequency and energy relationship, determine which type of electromagnetic radiation has the higher energy for each pair: (a) Infrared has higher energy than microwaves, (b) Visible light has higher energy than infrared, (c) X rays have higher energy than ultraviolet light, (d) Ultraviolet light has higher energy than visible light.

Key concepts

Electromagnetic Radiation

Electromagnetic radiation might sound complex, but it's actually a kind of energy that many of us encounter in everyday life. It takes the form of waves, and these waves carry energy as they travel through space. Although these waves are invisible to the naked eye, they have a significant impact on the world around us. For instance, the warmth you feel from the sun is due to electromagnetic radiation, specifically its infrared rays.

Electromagnetic radiation includes a wide range of wavelengths and frequencies. The term 'spectrum' refers to the entire range of electromagnetic wave types, which includes radio waves at one end with the longest wavelengths, through to gamma rays at the opposite end with the shortest wavelengths. Each type of wave has its own applications - for example, radio waves for broadcasting, and X-rays for medical imaging.

Wavelength and Frequency Relationship

When we talk about electromagnetic waves, two key terms often come up: wavelength and frequency. Wavelength is the distance between two corresponding points of consecutive waves, like peak to peak, and is usually measured in meters. Frequency, on the other hand, refers to how many waves pass a particular point in one second, measured in hertz (Hz).

Here's the crucial bit: frequency and wavelength are inversely related. This means that as the frequency increases, the wavelength gets shorter. And why does this matter? Because this relationship affects the energy of the waves. High-frequency electromagnetic waves have more energy than those with lower frequencies. So in the electromagnetic spectrum, shorter wavelengths correspond with higher energy levels.

Photon Energy

Let's dive deeper into what gives electromagnetic waves their punch. At a fundamental level, electromagnetic radiation can be thought of as a stream of 'packets' or particles known as photons. Each photon carries a certain amount of energy. This is where the term 'photon energy' comes in.

The energy of a photon is given by a simple formula: E = hν, where 'E' is the energy of the photon, 'h' is Planck’s constant (approximately 6.6261 x 10^-34 Joule seconds), and 'ν' (nu) is the frequency of the wave. Since the energy is directly proportional to frequency, this formula tells us that the higher the frequency of the electromagnetic wave, the more energy each photon carries. It's like the difference between being hit by a slow-moving tennis ball versus a fast-moving one - the faster it's moving (or the higher its frequency in the context of waves), the more energy it packs.

Comparing Electromagnetic Wavelengths

When comparing electromagnetic wavelengths, it's essential to understand that not all electromagnetic waves are created equal. Each type of wave, from radio to gamma rays, has its own distinct energy level due to its wavelength and frequency. For students, this can sometimes be a source of confusion.

Let's make it simpler with an example from the original exercise. Visible light waves, which enable us to see colors, have shorter wavelengths and higher frequencies compared to infrared waves, which we primarily sense as heat. Thus, visible light photons are more energetic than those of infrared radiation. This is why, in the question (b) from the exercise, visible light has higher energy than infrared. By understanding that a shorter wavelength means a higher frequency and therefore more energy, you can confidently determine which type of electromagnetic radiation has more energy in any given comparison.