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Ch.8 - The Quantum-Mechanical Model of the Atom
All textbooksTro 6th EditionCh.8 - The Quantum-Mechanical Model of the AtomProblem 96
Chapter 8, Problem 96

The distance from Earth to the sun is 1.5×108 km. Find the number of crests in a light wave of frequency 1.0×1014 s –1 traveling from the sun to Earth.

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Step 1: Understand that the number of crests in a light wave is equivalent to the number of wavelengths that pass a point in a given time. This is also known as the frequency of the wave.
Step 2: Convert the distance from Earth to the sun from kilometers to meters by multiplying by 1,000. This is because the speed of light is typically given in meters per second (m/s).
Step 3: Calculate the time it takes for light to travel from the sun to Earth by dividing the distance by the speed of light. The speed of light is approximately 3.0 * 10^8 m/s.
Step 4: Multiply the time it takes for light to travel from the sun to Earth by the frequency of the light wave to find the number of crests. This is because frequency is defined as the number of cycles (or crests) per unit of time.
Step 5: The result from step 4 is the number of crests in a light wave of the given frequency traveling from the sun to Earth.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Wave Properties

Light behaves as a wave, characterized by its wavelength and frequency. The relationship between these properties is described by the equation c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency. Understanding this relationship is crucial for calculating the number of wave crests over a given distance.
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Physical Properties

Speed of Light

The speed of light in a vacuum is approximately 3.0 x 10^8 meters per second. This constant speed is essential for determining how far light travels over a specific distance, such as from the sun to Earth. Knowing the speed allows us to relate time, distance, and the number of wave crests in a light wave.
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Speed of Light Formula

Calculating Wave Crests

To find the number of crests in a light wave traveling a certain distance, one can use the formula: Number of crests = Distance / Wavelength. First, the wavelength can be calculated using the speed of light and frequency. This concept is fundamental for quantifying how many complete cycles of the wave fit into the distance traveled.
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Electromagnetic Waves
Related Practice
Textbook Question

The speed of sound in air is 344 m/s at room temperature. The lowest frequency of a large organ pipe is 30 s–1 and the highest frequency of a piccolo is 1.5×104 s–1. Find the difference in wavelength between these two sounds.

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Textbook Question

A 5.00-mL ampule of a 0.100-M solution of naphthalene in hexane is excited with a flash of light. The naphthalene emits 12.3 J of energy at an average wavelength of 349 nm. What percentage of the naphthalene molecules emitted a photon?

Textbook Question

A laser produces 20.0 mW of red light. In 30.0 minutes, the laser emits 1.15×1020 photons. What is the wavelength of the laser?

Textbook Question

A particular laser consumes 140.0 watts of electrical power and produces a stream of 1.25×1019 1064-nm photons per second. What is the percent efficiency of the laser in converting electrical power to light?