Problem 16 - Chemistry: The Central Science in SI Units, Global Edition

Question

Determine which of the following statements are false and correct them. (a) The frequency of radiation increases as the wavelength increases. (b) Electromagnetic radiation travels through a vacuum at a constant speed, regardless of wavelength. (c) Infrared light has higher frequencies than visible light. (d) The glow from a fireplace, the energy within a microwave oven, and a foghorn blast are all forms of electromagnetic radiation.

Step-by-Step Solution

Answer

(a) False. Corrected: The frequency of radiation decreases as the wavelength increases. (b) True. (c) False. Corrected: Infrared light has lower frequencies than visible light. (d) Partially true. Corrected: The glow from a fireplace and the energy within a microwave oven are forms of electromagnetic radiation, while a foghorn blast is not.

Step 1: Statement (a) Analysis

The frequency of radiation increases as the wavelength increases. This statement claims that the frequency of electromagnetic radiation is directly proportional to the wavelength. However, from the formula for the speed of light, we know that the frequency is inversely proportional to the wavelength: \(c = \lambda\nu\) where c is the speed of light, λ is the wavelength, and ν is the frequency.

Step 2: Statement (a) Correction

The frequency of radiation decreases as the wavelength increases.

Step 3: Statement (b) Analysis

Electromagnetic radiation travels through a vacuum at a constant speed, regardless of wavelength. This statement is true. The speed of electromagnetic radiation in a vacuum remains constant, which is approximately 3 x 10^8 meters per second (the speed of light), regardless of wavelength.

Step 4: Statement (c) Analysis

Infrared light has higher frequencies than visible light. This statement is incorrect. Infrared light has lower frequencies than visible light. The electromagnetic spectrum is ordered from low frequencies to high frequencies, with the order being radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.

Step 5: Statement (c) Correction

Infrared light has lower frequencies than visible light.

Step 6: Statement (d) Analysis

The glow from a fireplace, the energy within a microwave oven, and a foghorn blast are all forms of electromagnetic radiation. This statement is partially true. The glow from a fireplace and the energy within a microwave oven are both forms of electromagnetic radiation in the infrared and microwave range, respectively. However, a foghorn blast is a form of sound wave, which is not part of the electromagnetic spectrum.

Step 7: Statement (d) Correction

The glow from a fireplace and the energy within a microwave oven are forms of electromagnetic radiation, while a foghorn blast is not.

Key Concepts

Wavelength and Frequency

In the electromagnetic spectrum, understanding the relationship between wavelength and frequency is important. These two properties are intricately linked in the realm of electromagnetic waves.
Imagine you are stretching a slinky. Wavelength refers to the distance between two consecutive peaks or troughs in a wave. On the other hand, frequency is the number of complete wave cycles that pass a fixed point in a given time period, usually one second.
This relationship can be mathematically described by the formula: \( c = \lambda u \) Here, \( c \) represents the speed of light, \( \lambda \) symbolizes the wavelength, and \( u \) denotes the frequency. This equation tells us:

• Wavelength \((\lambda)\) and frequency \((u)\) are inversely proportional.
• As the wavelength increases, the frequency decreases.
• Conversely, when the wavelength is shorter, the frequency is higher.

Understanding this inverse relationship helps explain why electromagnetic waves of different frequencies and wavelengths behave the way they do across the spectrum.

Speed of Light

The speed of light is a fundamental constant in physics that plays a pivotal role in our understanding of electromagnetic radiation. All electromagnetic waves, whether they are radio waves or gamma rays, travel at the same speed in a vacuum. This speed is approximately \(3 \times 10^8 \) meters per second (\(m/s\)).
Despite the variations in wavelength and frequency across the electromagnetic spectrum, the speed remains constant. This consistency is crucial because it allows us to use the wavelength and frequency interchangeably in various calculations, knowing that the product of these two will always equal the speed of light in a vacuum.
The notion that electromagnetic waves travel at this fixed speed independent of wavelength leads to important applications, like predicting how long it will take light from a star to reach us on Earth. Additionally, this unchanging speed forms the basis of Einstein's theory of relativity, which has radically transformed our understanding of time and space.

Forms of Radiation

Electromagnetic radiation can manifest in many forms, each varying in wavelength and frequency. The electromagnetic spectrum categorizes these diverse forms based on their frequencies and wavelengths.
Here’s a helpful way to visualize the hierarchy of radiation forms from longer wavelengths (lower frequencies) to shorter wavelengths (higher frequencies):

• Radio Waves
• Microwaves
• Infrared Radiation
• Visible Light
• Ultraviolet Light
• X-Rays
• Gamma Rays

Each type of radiation serves different functions and exists naturally in our world. For instance, radio waves are used in broadcasting; infrared radiation can be felt as heat; visible light is what we see; and X-rays are used in medical imaging. Understanding the distinctions in the forms of radiation is essential for their respective applications, which are pivotal in technology, medicine, and scientific research.