Problem 16 - Chemistry The Central Science In Si Units

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

Statements (a) and (c) are false. Statement (a) should describe decreasing frequency with increasing wavelength, and statement (c) should state that infrared light has lower frequencies than visible light. Statement (d) needs correction: only the fireplace glow and microwaves are electromagnetic, not sound from the foghorn.

Step 1: Clarify statement (a)

Statement (a) says: 'The frequency of radiation increases as the wavelength increases.' This statement is false. Frequency and wavelength are inversely related, as given by the formula \( c = \lambda u \), where \( c \) is the speed of light, \( \lambda \) is the wavelength, and \( u \) is the frequency. Hence, as the wavelength increases, the frequency actually decreases. The correct statement is: 'The frequency of radiation decreases as the wavelength increases.'

Step 2: Analyze statement (b)

Statement (b) mentions: 'Electromagnetic radiation travels through a vacuum at a constant speed, regardless of wavelength.' This statement is true. In a vacuum, all electromagnetic waves travel at the same speed, which is the speed of light, approximately \(3.00 \times 10^8\) m/s, regardless of their wavelength.

Step 3: Review statement (c)

Statement (c) claims: 'Infrared light has higher frequencies than visible light.' This statement is false. Infrared light actually has lower frequencies and longer wavelengths than visible light. The correct statement should be: 'Infrared light has lower frequencies than visible light.'

Step 4: Evaluate statement (d)

Statement (d) asserts: 'The glow from a fireplace, the energy within a microwave oven, and a foghorn blast are all forms of electromagnetic radiation.' This statement is partly true. The glow from a fireplace and the energy within a microwave oven are both forms of electromagnetic radiation (visible light and microwave radiation, respectively). However, a foghorn blast is a form of sound, which is a mechanical wave, not electromagnetic radiation. The corrected statement should be: 'The glow from a fireplace and the energy within a microwave oven are forms of electromagnetic radiation.'

Key Concepts

Frequency and Wavelength Relationship

The relationship between frequency and wavelength is fundamental in understanding electromagnetic waves. They are inversely related, which means when one increases, the other decreases. This relationship is best expressed mathematically by the equation: \[ c = \lambda u \] * \( c \) is the speed of light in a vacuum. * \( \lambda \) is the wavelength of the wave. * \( u \) is the frequency of the wave. Because the speed of light in a vacuum is constant, any change in the wavelength will inversely affect the frequency. For instance, if a wave has a shorter wavelength, it will have a higher frequency, and vice versa. Understanding this concept is crucial because it explains how different types of electromagnetic radiation, from radio waves to gamma rays, can all travel at the same speed but differ in frequency and wavelength. So, when you hear that the frequency of radiation decreases as the wavelength increases, it aligns precisely with this fundamental principle.

Speed of Light in Vacuum

Electromagnetic waves have a unique property—they travel through a vacuum at the same speed, commonly known as the speed of light. This speed is a universal constant and is approximately \( 3.00 \times 10^8 \) meters per second. Despite the differences in frequency and wavelength among various electromagnetic waves, like radio waves, microwaves, infrared, visible, ultraviolet, X-rays, and gamma rays, all travel at this constant speed in a vacuum. This constancy of speed is foundational in physics and is essential for understanding the behavior of light and other electromagnetic waves. It serves as the basis for Einstein's theory of relativity and affects how we measure distances in space. For students, it's important to remember that regardless of the type of electromagnetic radiation, when in a vacuum, the speed remains unchanged. Wavelengths may vary, and frequencies may differ, but speed does not waver. This is why the statement that electromagnetic radiation travels at a constant speed in a vacuum is true.

Infrared and Visible Light

When examining the electromagnetic spectrum, infrared and visible light fall into distinctive bands, each with its own characteristics. Infrared light is situated just beyond the visible spectrum, often associated with heat. It has longer wavelengths and thus lower frequencies compared to visible light. Visible light, on the other hand, consists of the colors we can see, ranging from violet (shorter wavelengths, higher frequencies) to red (longer wavelengths, lower frequencies). The order of colors in visible light reflects its range of wavelengths and frequencies. While infrared light is often used in applications like thermal imaging and remote controls, visible light is what illuminates our world and makes it possible for us to see. Understanding these differences is key because it affects how these types of light are used in technology and everyday life. It's crucial to correct any misconceptions, like the one about infrared light having higher frequencies than visible light—it's actually the other way around.