/*! 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 12 (a) What is the relationship bet... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 12

(a) What is the relationship between the wavelength and the frequency of radiant energy? (b) Ozone in the upper atmosphere absorbs energy in the \(210-230-\mathrm{nm}\) range of the spectrum. In what region of the electromagnetic spectrum does this radiation occur?

Short Answer

Expert verified
(a) Wavelength (位) and frequency (v) of radiant energy are inversely proportional to each other, as expressed by the equations \(位 = \frac{c}{v}\) and \(v = \frac{c}{位}\), where 'c' is the speed of light in a vacuum (\(3 脳 10^8\ \mathrm{m/s}\)). As the wavelength increases, the frequency decreases, and vice versa. (b) The given wavelength range of \(210-230\ \mathrm{nm}\) falls under the category of Ultraviolet radiation within the electromagnetic spectrum.

Step by step solution

01

(a) Wavelength and Frequency Relationship

The relationship between the wavelength (denoted as '位', in meters) and frequency (denoted as 'v' or 'f', in Hertz) of radiant energy can be described using the equation: \(c = 位v\) Here, 'c' represents the speed of light in a vacuum, which is approximately equal to \(3 脳 10^8\ \mathrm{m/s}\). To find the relationship between wavelength and frequency of radiant energy, isolate the variable of interest in this equation.
02

(a) Explain Wavelength and Frequency

Divide both sides of the equation \(c = 位v\) by the frequency 'v' to isolate the wavelength '位': \(位 = \frac{c}{v}\) Now, divide both sides of the equation \(c = 位v\) by the wavelength '位' to isolate the frequency 'v': \(v = \frac{c}{位}\) These equations show that wavelength and frequency are inversely proportional to each other while the speed of light remains constant. As the wavelength of radiant energy increases, its frequency decreases, and vice versa.
03

(b) Finding Electromagnetic Spectrum Region

The given range of the spectrum, where ozone in the upper atmosphere absorbs energy, is \(210-230\ \mathrm{nm}\). To identify the region of the electromagnetic spectrum that this radiation belongs to, refer to the classification of the electromagnetic spectrum based on wavelengths. Here is the classification: - Gamma Rays: < 0.01 nm - X-Rays: 0.01 nm - 10 nm - Ultraviolet: 10 nm - 400 nm - Visible Light: 400 nm - 700 nm - Infrared: 700 nm - 1 mm - Microwaves: 1 mm - 1 m - Radio Waves: > 1 m
04

(b) Determine the Radiation Region

As the given wavelength range is \(210-230\ \mathrm{nm}\), it can be observed that this range falls under the category of Ultraviolet radiation within the electromagnetic spectrum.

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 91影视!

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

(a) Why does the Bohr model of the hydrogen atom violate the uncertainty principle? (b) In what way is the description of the electron using a wave function consistent with de Broglie's hypothesis? (c) What is meant by the term probability density? Given the wave function, how do we find the probability density at a certain point in space?

The hydrogen atom can absorb light of wavelength \(2626 \mathrm{nm}\). (a) In what region of the electromagnetic spectrum is this absorption found? (b) Determine the initial and final values of \(n\) associated with this absorption.

Indicate whether energy is emitted or absorbed when the following electronic transitions occur in hydrogen: (a) from \(n=2\) to \(n=6,\) (b) from an orbit of radius \(4.76 \AA\) to one of radius \(0.529 \AA,(\mathrm{c})\) from the \(n=6\) to the \(n=9\) state.

(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.

The familiar phenomenon of a rainbow results from the diffraction of sunlight through raindrops. (a) Does the wavelength of light increase or decrease as we proceed outward from the innermost band of the rainbow? (b) Does the frequency of light increase or decrease as we proceed outward? (c) Suppose that instead of sunlight, the visible light from a hydrogen discharge tube (Figure 6.10 ) was used as the light source. What do you think the resulting "hydrogen discharge rainbow" would look like? [Section 6.3\(]\)
See all solutions

Recommended explanations on Chemistry Textbooks

Physical Chemistry

Read Explanation

Chemical Analysis

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Making Measurements

Read Explanation

Chemical Reactions

Read Explanation

The Earths Atmosphere

Read Explanation
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.