Ch.6 - Electronic Structure of Atoms

Brown - Chemistry: The Central Science 15th Edition

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Brown 15th Edition

Ch.6 - Electronic Structure of Atoms

Problem 43a

Chapter 6, Problem 43a

One of the emission lines of the hydrogen atom has a wavelength of 93.07 nm. a. In what region of the electromagnetic spectrum is this emission found?

Verified step by step guidance

insert step 1> Convert the given wavelength from nanometers to meters by using the conversion factor: 1 nm = 1 x 10^{-9} m.

insert step 2> Recall the regions of the electromagnetic spectrum and their corresponding wavelength ranges.

insert step 3> Compare the converted wavelength to the known ranges of the electromagnetic spectrum to determine the region.

insert step 4> Identify the region of the electromagnetic spectrum that corresponds to the given wavelength.

insert step 5> Conclude which part of the electromagnetic spectrum the emission line belongs to based on the comparison.

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Key Concepts

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

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, arranged by wavelength or frequency. It includes various regions such as radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. Each region has distinct properties and applications, with wavelengths ranging from kilometers for radio waves to picometers for gamma rays.

Wavelength and Frequency

Wavelength is the distance between successive peaks of a wave, typically measured in nanometers (nm) for light. Frequency, measured in hertz (Hz), indicates how many wave peaks pass a point in one second. The relationship between wavelength and frequency is inversely proportional, described by the equation c = λν, where c is the speed of light, λ is wavelength, and ν is frequency.

Ultraviolet Radiation

Ultraviolet (UV) radiation is a type of electromagnetic radiation with wavelengths shorter than visible light, typically ranging from about 10 nm to 400 nm. The specific wavelength of 93.07 nm falls within the extreme ultraviolet (EUV) region, which is known for its high energy and ability to ionize atoms. UV radiation has various applications, including sterilization and phototherapy, but can also pose health risks.

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Related Practice

Textbook Question

One of the emission lines of the hydrogen atom has a wavelength of 93.07 nm. b. Determine the initial and final values of n associated with this emission.

Textbook Question

The Lyman series of emission lines of the hydrogen atom are those for which nf = 1. (a) Determine the region of the electromagnetic spectrum in which the lines of the Lyman series are observed.

Textbook Question

The visible emission lines observed by Balmer all involved nf = 2. (b) Calculate the wavelengths of the first three lines in the Balmer series—those for which ni = 3, 4, and 5—and identify these lines in the emission spectrum shown in Figure 6.11.

Textbook Question

Order the following transitions in the hydrogen atom from smallest to largest frequency of light absorbed: n = 3 to n = 6, n = 4 to n = 9, n = 2 to n = 3, and n = 1 to n = 2.

Textbook Question

The Lyman series of emission lines of the hydrogen atom are those for which nf = 1. (b) Calculate the wavelengths of the first three lines in the Lyman series—those for which ni = 2, 3, and 4.

Textbook Question

The hydrogen atom can absorb light of wavelength 1094 nm. (b) Determine the final value of n associated with this absorption.