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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) The frequency of radiation increases as the wavelength increases. (c) Ultraviolet light has longer wavelengths than visible light. (d) X-rays travel faster than microwaves. (e) Electromagnetic radiation and sound waves travel at the same speed.

Short Answer

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(a) True. Visible light is a form of electromagnetic radiation. (b) False. The frequency of radiation decreases as the wavelength increases. (c) False. Ultraviolet light has shorter wavelengths than visible light. (d) False. X-rays and microwaves travel at the same speed, which is the speed of light. (e) False. Electromagnetic radiation travels faster than sound waves.

Step by step solution

01

(a) Visible light is a form of electromagnetic radiation.

This statement is True. Visible light is indeed a form of electromagnetic radiation, which is a range of energy waves that can be found on the electromagnetic spectrum. Other types of electromagnetic radiation include radio waves, microwaves, infrared, ultraviolet, X-rays, and gamma rays.
02

(b) The frequency of radiation increases as the wavelength increases.

This statement is False. The correct statement is: The frequency of radiation decreases as the wavelength increases. Frequency and wavelength have an inverse relationship, which is given by the formula: \(v = \lambda f\), where \(v\) is the speed of light in a vacuum, \(\lambda\) is the wavelength, and \(f\) is the frequency.
03

(c) Ultraviolet light has longer wavelengths than visible light.

This statement is False. The correct statement is: Ultraviolet light has shorter wavelengths than visible light. On the electromagnetic spectrum, ultraviolet light has wavelengths between about 10 nanometers and 400 nanometers, while visible light has wavelengths between about 400 nanometers and 700 nanometers.
04

(d) X-rays travel faster than microwaves.

This statement is False. The correct statement is: X-rays and microwaves travel at the same speed. Both types of electromagnetic radiation travel at the speed of light, which is approximately \(3.00 \times 10^8\) meters per second in a vacuum. Their wavelengths and frequencies differ, but their speed remains the same.
05

(e) Electromagnetic radiation and sound waves travel at the same speed.

This statement is False. The correct statement is: Electromagnetic radiation travels faster than sound waves. Electromagnetic radiation, such as light, travels at the speed of light, which is about \(3.00 \times 10^8\) meters per second in a vacuum. Sound waves, on the other hand, are mechanical waves that travel through a medium like air or water, and their speed depends on the properties of the medium. In air at room temperature, sound waves travel at approximately 343 meters per second, which is much slower than the speed of light.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Properties of Light
Light is one of the most familiar forms of electromagnetic radiation, visible to the human eye. It possesses remarkable properties that enable us to see the world around us. First and foremost, light behaves both as a wave and as a particle, a concept known as wave-particle duality. As a wave, it is characterized by its wavelength and frequency, and as a particle, it is referred to as a photon.

Light travels through a vacuum at a constant speed, approximately \(3.00 \times 10^8\) meters per second. This incredible speed allows it to cover vast distances in space almost instantaneously compared to human perception. Moreover, light can travel through various mediums, such as water or glass, though at different speeds depending on the medium's properties.

Another essential property of light is its ability to be refracted and reflected. Refraction occurs when light changes direction as it passes from one medium to another, while reflection happens when light bounces off a surface. These properties are fundamental for lenses and mirrors to function, consequently leading to the development of numerous optical devices, from eyeglasses to telescopes.
Frequency and Wavelength Relationship
The relationship between frequency and wavelength is a cornerstone concept in understanding electromagnetic radiation. This relationship is inversely proportional, meaning as the wavelength of the light increases, its frequency decreases, and vice versa. The formula \(v = \lambda f\) expresses this relationship, where \(v\) is the speed of light, \(\lambda\) is the wavelength, and \(f\) is the frequency.

Whenever light travels through a vacuum, its speed remains constant, thus any changes in wavelength will directly affect the frequency. A longer wavelength corresponds to a lower frequency which, for example, results in the reddish hues that we see. Conversely, a shorter wavelength translates to a higher frequency, bringing about the vivid violet colors.

The inverse relationship between wavelength and frequency is vital in numerous applications, including telecommunications, where the spectrum is allocated based on frequencies and medicine, such as in the use of different wavelengths for various diagnostic imaging techniques.
Electromagnetic Spectrum
The electromagnetic spectrum is a vast and continuous range of frequencies and wavelengths of electromagnetic radiation. This spectrum includes, in order of increasing frequency and decreasing wavelength: radio waves, microwaves, infrared radiation, visible light, ultraviolet light, X-rays, and gamma rays.

Each type of electromagnetic radiation has unique properties and uses. For instance, radio waves are widely utilized in communication systems; microwaves are perfect for heating food; infrared is crucial in remote controls and thermal imaging; visible light allows us to perceive colors; ultraviolet light helps the body produce vitamin D; X-rays are indispensable in medical imaging; and gamma rays are used in cancer treatment.

Understanding the electromagnetic spectrum enables us to harness different types of radiation for various technologies, which have become integral parts of our daily lives, as well as to understand natural phenomena such as the emission spectra of stars.
Comparison of Wave Speeds
There are common misconceptions about the speeds of various waves. All electromagnetic radiation, whether it be visible light, radio waves, microwaves, or X-rays, travels at the same speed in a vacuum: approximately \(3.00 \times 10^8\) meters per second. This is the universal speed of light, a constant \(c\) in Einstein's famous equation \(E=mc^2\).

However, when electromagnetic radiation passes through a medium other than a vacuum, such as air or water, its speed is reduced due to the interaction with the medium's particles. For example, light slows down when it travels through water, which results in the bending of light, known as refraction.

In contrast, sound waves, which are mechanical waves requiring a medium to travel, such as air, water, or solids, move much slower. In room-temperature air, sound travels at about 343 meters per second, far slower than light. This significant difference in speeds helps explain phenomena like thunder and lightning: we see the lightning before we hear the thunder because light reaches us much quicker than sound.

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Most popular questions from this chapter

(a) Using Equation \(6.5\), calculate the energy of an electron in the hydrogen atom when \(n=2\) and when \(n=6\). Calculate the wavelength of the radiation released when an electron moves from \(n=6\) to \(n=2\). Is this line in the visible region of the electromagnetic spectrum? If so, what color is it? (b) Calculate the energies of an electron in the hydrogen atom for \(n=1\) and for \(n=(\infty)\). How much energy does it require to move the electron out of the atom completely (from \(n=1\) to \(n=\infty\) ), according to Bohr? Put your answer in \(\mathrm{kJ} / \mathrm{mol}\). (c) The energy for the process \(\mathrm{H}+\) energy \(\rightarrow \mathrm{H}^{+}+\mathrm{e}^{-}\) is called the ionization energy of hydrogen. The experimentally determined value for the ionization energy of hydrogen is \(1310 \mathrm{~kJ} / \mathrm{mol}\). How does this compare to your calculation?

The first 25 years of the twentieth century were momentous for the rapid pace of change in scientists' understanding of the nature of matter. (a) How did Rutherford's experiments on the scattering of \(\alpha\) particles by a gold foil set the stage for Bohr's theory of the hydrogen atom? (b) In what ways is de Broglie's hypothesis, as it applies to electrons, consistent with J. J. Thomson's conclusion that the electron has mass? In what sense is it consistent with proposals that preceded Thomson's work, that the cathode rays are a wave phenomenon?

(a) In terms of the Bohr theory of the hydrogen atom, what process is occurring when excited hydrogen atoms emit radiant energy of certain wavelengths and only those wavelengths? (b) Does a hydrogen atom "expand" or "contract" as it moves from its ground state to an excited state?

Which of the quantum numbers governs (a) the shape of an orbital, (b) the energy of an orbital, (c) the spin properties of the electron, (d) the spatial orientation of the orbital?

(a) The average distance from the nucleus of a 3 s electron in a chlorine atom is smaller than that for a \(3 p\) electron. In light of this fact, which orbital is higher in energy? (b) Would you expect it to require more or less energy to remove a \(3 s\) electron from the chlorine atom, as compared with a \(2 p\) electron? Explain.

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