/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 77 The different colors of light ha... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

The different colors of light have different wavelengths. The human eye is most sensitive to light whose wavelength is \(555 \mathrm{~nm}\) ( greenish- yellow). What is this wavelength in centimeters?

Short Answer

Expert verified
The wavelength is \(5.55 \times 10^{-5}\) cm.

Step by step solution

01

Understand the Problem

We need to convert a wavelength given in nanometers (nm) to centimeters (cm). We know that 1 nm is equal to \(10^{-9}\) meters.
02

Convert Nanometers to Meters

First, convert the wavelength from nanometers to meters. The given wavelength is \(555\) nm. Since \(1 \text{ nm} = 10^{-9} \text{ m}\), the conversion is: \[555 \text{ nm} = 555 \times 10^{-9} \text{ m}\].
03

Convert Meters to Centimeters

Now, convert from meters to centimeters. Remember, 1 meter is equivalent to 100 centimeters:\[555 \times 10^{-9} \text{ m} = 555 \times 10^{-9} \times 100 \text{ cm}\].Perform the calculation to find:\[555 \times 10^{-7} \text{ cm} = 5.55 \times 10^{-5} \text{ cm}\].

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Nanometer to Centimeter Conversion
When working with wavelengths, you often see measurements in nanometers (nm) due to the small size of light waves. However, sometimes it is more convenient to express these measurements in other units, such as centimeters (cm). Converting from nanometers to centimeters involves a two-step process:
  • Convert nanometers to meters, as a nanometer is billionths of a meter.
  • Then convert from meters to centimeters, remembering that 1 meter equals 100 centimeters.
Starting with our example of a wavelength of 555 nm, we begin by changing nanometers to meters. Since 1 nm is equivalent to \(10^{-9}\) meters, the conversion looks like this: \[555 ext{ nm} = 555 imes 10^{-9} ext{ m}\]. Next, we convert the measure in meters to centimeters. Since 1 meter equals 100 centimeters, multiply by 100: \[555 imes 10^{-9} ext{ m} = 555 imes 10^{-9} imes 100 ext{ cm}\].This results in a final answer of \(5.55 \times 10^{-5} \text{ cm}\). Breaking the conversion into these steps makes sure all details are clearly understood.
Light Wavelength
Light is a fascinating subject. Each color of light is identified by its own unique wavelength. In the visible spectrum, wavelengths vary from violet (around 380 nm) to red (around 700 nm). The human eye is particularly sensitive to the wavelength around 555 nm, which is a greenish-yellow color. Light's behavior, such as how it bends or reflects, is tied closely to its wavelength. These differences play a crucial role in understanding diverse phenomena like rainbows, the color of the sky, and even technology like cameras and displays. Even a tiny change in the wavelength can affect the color we perceive.
Understanding the concept of light wavelength is key for everything from astronomy to art, providing insights into both the natural world and human technology.
Units of Measurement
Units are the foundation for expressing quantities in science and everyday life. They offer a way to communicate clearly and ensure everyone understands the magnitude of what's being discussed. In physics and other sciences, using the correct units of measurement is vital.
  • Nanometers (nm) are often used to describe wavelengths in the electromagnetic spectrum due to their tiny scale.
  • Meters (m) provide a standard base unit in the metric system, making them easy to convert into other units like centimeters (cm) or kilometers (km).
  • Centimeters (cm), on the other hand, offer a size more relatable for everyday measurements.
The conversion between these units shows the convenience of the metric system. For example, recognizing that 1 nanometer is \(10^{-9}\) meters provides an easy transformation from microscopic to macroscopic perspectives. Understanding and using these conversions and units help in scientific calculations, ensuring accuracy and clarity in communication.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The land area of Greenland is \(840,000 \mathrm{mi}^{2}\), with only \(132,000 \mathrm{mi}^{2}\) free of perpetual ice. The average thickness of this ice is \(5000 \mathrm{ft}\). Estimate the mass of the ice (assume two significant figures). The density of ice is \(0.917 \mathrm{~g} / \mathrm{cm}^{3}\).

Zinc ore (zinc sulfide) is treated with sulfuric acid, leaving a solution with some undissolved bits of material and releasing hydrogen sulfide gas. If \(10.8 \mathrm{~g}\) of zinc ore is treated with \(50.0 \mathrm{~mL}\) of sulfuric acid (density \(1.153 \mathrm{~g} / \mathrm{mL}\) ), \(65.1 \mathrm{~g}\) of solution and undissolved material remains. In addition, hydrogen sulfide (density \(1.393 \mathrm{~g} / \mathrm{L}\) ) is evolved. What is the volume (in liters) of this gas?

Obtain the difference in volume between two spheres, one of radius \(5.61 \mathrm{~cm}\), the other of radius \(5.85 \mathrm{~cm}\). The volume \(V\) of a sphere is \((4 / 3) \pi r^{3}\), where \(r\) is the radius. Give the result to the correct number of significant figures.

The acidic constituent in vinegar is acetic acid. A 10.0-mL sample of a certain vinegar contains \(501 \mathrm{mg}\) of acetic acid. What is this mass of acetic acid expressed in micrograms?

Mercury(II) oxide is an orange-red solid with a density of \(11.1 \mathrm{~g} / \mathrm{cm}^{3} .\) It decomposes when heated to give mercury and oxygen. The compound is insoluble in water (does not dissolve in water). Identify the physical and the chemical properties of mercury(II) oxide that are cited.

See all solutions

Recommended explanations on Chemistry Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.