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Chapter 5: Problem 3

Why do we say that light is an electromagnetic wave? Describe the relationship among wavelength, frequency, and speed for light.

Short Answer

Expert verified
Light is an electromagnetic wave due to its oscillating electric and magnetic fields. The equation \( c = \lambda \cdot f \) describes the relationship among wavelength \( \lambda \), frequency \( f \), and speed \( c \) for light.

Step by step solution

01

Understand Light as a Wave

Light is considered an electromagnetic wave because it consists of oscillating electric and magnetic fields, which are perpendicular to each other and to the direction of propagation. These fields move through space, transmitting energy without requiring a medium, unlike sound waves.
02

Identify the Components of the Wave

An electromagnetic wave like light is characterized by its wavelength (\( \lambda \)), frequency (\( f \)), and speed (\( c \)). Wavelength is the distance between consecutive crests of the wave, frequency is the number of waves that pass a given point per second, and speed is how fast the wave propagates through a medium.
03

Understand the Wave Equation

The relationship between wavelength, frequency, and speed for light is expressed by the equation \( c = \lambda \cdot f \), where \( c \) is the speed of light in vacuum, approximately \( 3 \times 10^8 \text{ meters per second} \). This equation shows that the speed of light is the product of its wavelength and frequency.
04

Explore the Implications of the Equation

Since the speed of light in a vacuum is constant, if the wavelength increases, the frequency must decrease to maintain the equality \( c = \lambda \cdot f \), and vice versa. This inverse relationship means that light with a longer wavelength has a lower frequency and light with a shorter wavelength has a higher frequency.

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Key Concepts

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

Wavelength
Wavelength is a fundamental property of electromagnetic waves, including light. It is defined as the distance between two consecutive peaks or troughs in a wave, commonly measured in meters or nanometers.
Wavelength gives us information about the energy and type of electromagnetic wave we are dealing with. Longer wavelengths, like that of radio waves, have lower energy, while shorter wavelengths, such as gamma rays, have higher energy.
  • Visible light, which humans can see, ranges from about 400 to 700 nm in wavelength.
  • Red light has a longer wavelength, while violet light has a shorter wavelength within the visible spectrum.
Understanding wavelength is crucial because it helps us to differentiate between various types of electromagnetic waves.
Frequency
Frequency is another key aspect of electromagnetic waves. It refers to the number of complete wave cycles that pass a given point per second. Frequency is measured in hertz (Hz), where one hertz equals one cycle per second.
A higher frequency means more wave cycles pass per second, which generally corresponds to higher energy. This is why ultraviolet light, which has a higher frequency than visible light, can cause sunburn.
  • Frequency is inversely related to wavelength in electromagnetic waves.
  • As the wavelength increases, the frequency decreases, and vice versa.
This is an essential concept because knowing the frequency allows us to calculate other vital properties, like energy and type of wave.
Speed of Light
The speed of light is a constant in a vacuum, generally fixed at approximately 3 x 10^8 meters per second. This is one of the cornerstones of physics, as it affects the behavior of electromagnetic waves, like light, in various mediums.
Light travels at this incredible speed because of its nature as an electromagnetic wave, which doesn't need a medium to propagate.
  • The equation connecting speed, wavelength, and frequency is: \( c = \lambda \cdot f \).
  • In different media, like water or glass, light can slow down, altering its wavelength but not its frequency.
Knowing the speed of light is essential for understanding how light and other electromagnetic waves interact with matter, help in technologies like GPS, and even explore the vastness of space.

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Most popular questions from this chapter

Be sure to show all calculations clearly and state your final answers in complete sentences. Doppler Calculations. In hydrogen, the transition from level 2 to level 1 has a rest wavelength of \(121.6 \mathrm{nm}\). Find the speed and direction (toward or away from us) of a star in which this line appears at wavelength a. \(120.5 \mathrm{nm} .\) b. \(121.2 \mathrm{nm} .\) c. \(121.9 \mathrm{nm} .\) d. \(122.9 \mathrm{nm}\)

Be sure to show all calculations clearly and state your final answers in complete sentences. How Many Photons? Suppose that all the energy from a 100 -watt light bulb came in the form of photons with wavelength \(600 \mathrm{nm}\). (This is not quite realistic; see Problem \(57 .\) ) a. Calculate the energy of a single photon with wavelength \(600 \mathrm{nm} .\) b. How many 600 -nm photons must be emitted each second to account for all the light from this 100 -watt light bulb? c. Based on your answer to part b, explain why we don't notice the particle nature of light in our everyday lives.

Atomic Terminology Practice II. a. What are the atomic number and atomic mass number of a fluorine atom with 9 protons and 10 neutrons? If we could add a proton to this fluorine nucleus, would the result still be fluorine? What if we added a neutron to the fluorine nucleus? Explain. b. The most common isotope of gold has atomic number 79 and atomic mass number \(197 .\) How many protons and neutrons does the gold nucleus contain? If the isotope is electrically neutral, how many electrons does it have? If it is triply ionized, how many electrons does it have? \(\mathbf{c} .\) Uranium has atomic number \(92 .\) Its most common isotope is \(^{238} \mathrm{U}\), but the form used in nuclear bombs and nuclear power plants is \(^{235} \mathrm{U}\). How many neutrons are in each of these two isotopes of uranium?

Be sure to show all calculations clearly and state your final answers in complete sentences. \(U V\) Photon. What is the energy (in joules) of an ultraviolet photon with wavelength \(120 \mathrm{nm}\) ? What is its frequency?

Be sure to show all calculations clearly and state your final answers in complete sentences. Electric Bill. Your electric utility bill probably shows your energy use for the month in units of kilowatthours. A kilowatt-hour is defined as the energy used in 1 hour at a rate of 1 kilowatt \((1000\) watts); that is, 1 kilowatt-hour \(=1\) kilowatt \(\times 1\) hour. Use this fact to convert 1 kilowatt-hour into joules. If your bill says you used 900 kilowatt- hours, how much energy did you use in joules?
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