Problem 15 - Chemistry: The Central Science

Question

Label each of the following statements as true or false. For those that are false, correct the statement. (a) Visible light is a form of electromagnetic radiation. (b) Ultraviolet light has longer wavelengths than visible light. (c) \(\mathrm{X}\) rays travel faster than microwaves. (d) Electromagnetic radiation and sound waves travel at the same speed.

Step-by-Step Solution

Answer

(a) True. Visible light is a form of electromagnetic radiation. (b) False. Corrected statement: Ultraviolet light has shorter wavelengths than visible light. (c) False. Corrected statement: X rays travel at the same speed as microwaves. (d) False. Corrected statement: Electromagnetic radiation and sound waves travel at different speeds.

Step 1: (a) Analyzing statement (a)#

To determine whether visible light is a form of electromagnetic radiation, we need to recall the definition and properties of electromagnetic radiation. Electromagnetic radiation refers to the different types of energy-carrying waves that can travel through space, such as radio waves, microwaves, infrared waves, visible light, ultraviolet light, X rays, and gamma rays. Knowing this, we can deduce whether or not visible light is a form of electromagnetic radiation.#

Step 2: (a) Conclusion for statement (a)#

Since visible light is included in the list of electromagnetic radiation types, statement (a) is true. Visible light is a form of electromagnetic radiation.

Step 3: (b) Analyzing statement (b)#

To evaluate statement (b), we need to compare the wavelengths of ultraviolet light and visible light. Wavelength is a property of electromagnetic waves which determines their energy and characteristics. Generally, the shorter the wavelength of an electromagnetic wave, the higher its energy.#

Step 4: (b) Conclusion for statement (b)#

Ultraviolet light has a shorter wavelength (in the range of 10 to 400 nm) than visible light (with wavelengths between 400 and 700 nm). Thus, statement (b) is false. The correct version of the statement is: Ultraviolet light has shorter wavelengths than visible light.

Step 5: (c) Analyzing statement (c)#

To analyze statement (c), we need to compare the speeds of X rays and microwaves. The speed of an electromagnetic wave refers to how fast it travels in a vacuum. Electromagnetic waves, including X rays and microwaves, travel at the same speed in a vacuum – the speed of light.#

Step 6: (c) Conclusion for statement (c)#

Since all electromagnetic waves travel at the same speed in a vacuum, statement (c) is false. The correct version of the statement is: X rays travel at the same speed as microwaves.

Step 7: (d) Analyzing statement (d)#

To evaluate statement (d), we need to compare the speeds of electromagnetic radiation and sound waves. Electromagnetic waves travel at the speed of light, whereas sound waves are mechanical waves that travel at a different speed in different media.#

Step 8: (d) Conclusion for statement (d)#

The speed of electromagnetic radiation (the speed of light in a vacuum) is much faster than the speed of sound waves in any medium. Therefore, statement (d) is false. The correct version of the statement is: Electromagnetic radiation and sound waves travel at different speeds.

Key Concepts

Visible Light

When we talk about visible light, we're referring to the portion of the electromagnetic spectrum that can be detected by the human eye. This form of electromagnetic radiation allows us to perceive the world in color. Visible light wavelengths range from about 400 to 700 nanometers (nm), with violet light at the shorter end of the spectrum and red light at the longer end.

Each color of visible light has its own unique wavelength. For instance, when sunlight passes through a prism, it is dispersed into a spectrum of colors, which is effectively separating light into its component wavelengths. This phenomenon, known as dispersion, reveals the colorful spectrum of visible light.

Wavelengths

The concept of wavelengths is central to understanding electromagnetic radiation. A wavelength is the distance between successive peaks of a wave. It's measured in units like meters, centimeters, or more commonly for light, nanometers. Different types of electromagnetic waves have different wavelengths, which determines their properties and how they interact with matter. For example, shorter wavelengths, like those of X-rays, have higher energy and can penetrate materials more easily compared to longer wavelengths, such as radio waves.

It's important to recognize that wavelength and frequency are inversely related; as the wavelength decreases, the frequency (how often the wave peaks pass a point in a given period of time) increases. This relationship means that each type of electromagnetic wave, from radio waves to gamma rays, has its own characteristic energy based on its wavelength and frequency.

Speed of Light

The speed of light is a fundamental constant of nature that plays a crucial role in physics and astronomy. In a vacuum, light travels at a mind-boggling speed of approximately 299,792 kilometers per second (about 186,282 miles per second). This speed is also the cosmic speed limit; according to Einstein's theory of relativity, no object with mass can travel faster than light.

Interestingly, while light travels at this constant speed in a vacuum, it slows down when it passes through various media like glass or water due to a process called refraction. This slowing down causes the light to bend, and it's the principle behind lenses, prisms, and even our own eyes' ability to focus.

Sound Waves

Unlike electromagnetic waves such as visible light, sound waves are mechanical waves that require a medium to travel through, like air, water, or solid materials. Sound waves are created by the vibration of objects and propagate through the medium as longitudinal waves, where the particle movement is parallel to the direction of wave travel.

One of the most interesting aspects of sound waves is their speed, which varies depending on the medium. For example, sound travels faster in water than in air, and even faster in solids. The speed of sound in air at room temperature is approximately 343 meters per second (1,125 feet per second), significantly slower than the speed of light in a vacuum.