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Chapter 6: Problem 2

What are the units for wavelength and frequency of electromagnetic waves? What is the speed of light in meters per second and miles per hour?

Short Answer

Expert verified
Wavelength is measured in meters; frequency in hertz. The speed of light is about 299,792,458 m/s or 670,616,629 mph.

Step by step solution

01

Understand the Concept of Wavelength and Frequency

Wavelength and frequency are properties of electromagnetic waves. Wavelength is the distance between consecutive crests (or troughs) of a wave, while frequency is the number of waves that pass a point in one second. Both terms are fundamental concepts in physics.
02

Units of Wavelength

The wavelength of electromagnetic waves is typically measured in meters (m). However, depending on the type of electromagnetic wave (e.g., radio waves, visible light, etc.), wavelengths can also be expressed in nanometers (nm), micrometers (碌m), or other length units.
03

Units of Frequency

Frequency is measured in hertz (Hz), where 1 Hz is equal to one cycle per second. In terms of measurement, frequency indicates how many complete wave cycles occur in one second.
04

Speed of Light in Meters Per Second

The speed of light in a vacuum is a constant and is approximately 299,792,458 meters per second (m/s). This value is often rounded to 3 脳 10^8 m/s for simplicity in calculations.
05

Convert Speed of Light to Miles Per Hour

To convert the speed of light from meters per second to miles per hour, use the conversion factors: 1 meter = 0.000621371 miles and 1 hour = 3600 seconds. Thus, the speed of light in miles per hour can be calculated as follows:\[ 299,792,458 ext{ m/s} imes 0.000621371 ext{ miles/m} imes 3600 ext{ seconds/hour} = 670,616,629 ext{ miles per hour} \]

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Key Concepts

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

Understanding Units of Wavelength
Wavelengths are essential for identifying the characteristics of electromagnetic waves. The most standard unit for measuring wavelength is the meter (m), which accommodates a wide range of applications. However, different fields and types of electromagnetic waves may require more specific measurements:
  • Nanometers (nm) - often used when dealing with visible light. 1 nm is equal to 10-9 meters.
  • Micrometers (碌m) - handy for infrared waves. 1 碌m is equal to 10-6 meters.
  • Millimeters (mm) - generally used in the context of radio waves. 1 mm equals 10-3 meters.
Choosing the right unit helps in accurately describing the wave, based on its usage or scientific requirement.
Comprehending Units of Frequency
Frequency tells us how often a wave oscillates per second and is key in understanding wave behavior. The fundamental unit of frequency is the hertz (Hz):
  • 1 Hertz (Hz) signifies one complete wave cycle per second.
  • Kilohertz (kHz) represents 1,000 cycles per second, often used in radio broadcasting.
  • Megahertz (MHz) corresponds to 1,000,000 cycles per second and is used for television broadcasts and microwaves.
  • Gigahertz (GHz) is 1,000,000,000 cycles per second, utilized in modern communications technology like Wi-Fi.
Different contexts require different frequency units, making it a versatile measurement in wave analysis.
Speed of Light in Meters Per Second
In physics, the speed of light is a critical constant denoting how fast light travels in a vacuum. This speed is approximately 299,792,458 meters per second (m/s). It is so pivotal that scientists often use the rounded value of 3 脳 108 m/s to simplify calculations without significantly affecting accuracy. This constant speed is the foundation for many equations and laws in physics, especially in relativity theory and electromagnetic theory.
Conversion of Speed of Light to Miles Per Hour
While the metric system is extensively used in scientific contexts, converting the speed of light to miles per hour can be useful, especially in applications involving speed comparisons over long distances. To perform this conversion:
  • Firstly, note that 1 meter is equivalent to 0.000621371 miles.
  • Also, there are 3,600 seconds in an hour.
Therefore, when translated to miles per hour, the speed of light is calculated as follows:\[ 299,792,458 \text{ m/s} \times 0.000621371 \text{ miles/m} \times 3600 \text{ seconds/hour} = 670,616,629 \text{ miles per hour} \]This massive number illustrates the incredible speed at which light can travel long distances in a blink of an eye.

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Most popular questions from this chapter

A particular form of electromagnetic radiation has a frequency of \(9.87 \times 10^{15} \mathrm{~Hz}\). (a) What is its wavelength in nanometers? In meters? (b) To what region of the electromagnetic spectrum would you assign it? (c) What is the energy (in joules) of one quantum of this radiation?

What are the group and period of the element osmium?

A ruby laser produces radiation of wavelength \(633 \mathrm{nm}\) in pulses whose duration is \(1.00 \times 10^{-9} \mathrm{~s}\). (a) If the laser produces \(0.376 \mathrm{~J}\) of energy per pulse, how many photons are produced in each pulse? (b) Calculate the power (in watts) delivered by the laser per pulse \((1 \mathrm{~W}=1 \mathrm{~J} / \mathrm{s}).\)

Which orbital in each of the following pairs is lower in energy in a many- electron atom: (a) \(2 s, 2 p\); (b) \(3 p, 3 d\) (c) \(3 s, 4 s ;\) d) \(4 d, 5 f\) ?

(a) An electron in the ground state of the hydrogen atom moves at an average speed of \(5 \times 10^{6} \mathrm{~m} / \mathrm{s}\). If the speed is known to an uncertainty of 20 percent, what is the minimum uncertainty in its position? Given that the radius of the hydrogen atom in the ground state is \(5.29 \times 10^{-11} \mathrm{~m},\) comment on your result. The mass of an electron is \(9.1094 \times 10^{-31} \mathrm{~kg} .\) (b) A \(0.15-\mathrm{kg}\) baseball thrown at 100 mph has a momentum of \(6.7 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}\). If the uncertainty in measuring the momentum is \(1.0 \times 10^{-7}\) of the momentum, calculate the uncertainty in the baseball's position.
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