Textbook Question
One of the emission lines of the hydrogen atom has a wavelength of 94.974 nm. (a) In what region of the electromagnetic spectrum is this emission found?
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Ch.6 - Electronic Structure of Atoms
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232
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Table of contents
- Ch.1 - Introduction: Matter, Energy, and Measurement140
- Ch.2 - Atoms, Molecules, and Ions192
- Ch.3 - Chemical Reactions and Reaction Stoichiometry172
- Ch.4 - Reactions in Aqueous Solution156
- Ch.5 - Thermochemistry151
- Ch.6 - Electronic Structure of Atoms137
- Ch.7 - Periodic Properties of the Elements127
- Ch.8 - Basic Concepts of Chemical Bonding143
- Ch.9 - Molecular Geometry and Bonding Theories167
- Ch.10 - Gases147
- Ch.11 - Liquids and Intermolecular Forces97
- Ch.12 - Solids and Modern Materials129
- Ch.13 - Properties of Solutions126
- Ch.14 - Chemical Kinetics175
- Ch.15 - Chemical Equilibrium107
- Ch.16 - Acid-Base Equilibria127
- Ch.17 - Additional Aspects of Aqueous Equilibria133
- Ch.18 - Chemistry of the Environment88
- Ch.19 - Chemical Thermodynamics140
- Ch.20 - Electrochemistry137
- Ch.21 - Nuclear Chemistry99
- Ch.22 - Chemistry of the Nonmetals66
- Ch.23 - Transition Metals and Coordination Chemistry69
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry11
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
Chapter 6, Problem 42a
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.
Verified step by step guidance1
Identify the Lyman series in the context of the hydrogen atom's emission spectrum, where the final energy level (n_f) is 1.
Recall that the Lyman series involves electronic transitions from higher energy levels (n_i > 1) to the n_f = 1 level.
Use the Rydberg formula for hydrogen: \( \frac{1}{\lambda} = R_H \left( \frac{1}{1^2} - \frac{1}{n_i^2} \right) \), where \( R_H \) is the Rydberg constant and \( n_i \) is the initial energy level.
Recognize that the Lyman series transitions result in the release of photons with wavelengths in the ultraviolet (UV) region of the electromagnetic spectrum.
Conclude that the Lyman series lines are observed in the ultraviolet region, as these transitions involve high energy changes.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Lyman Series
The Lyman series refers to a set of spectral lines corresponding to transitions of electrons in a hydrogen atom from higher energy levels (n ≥ 2) to the lowest energy level (n = 1). These transitions result in the emission of ultraviolet light, which is a key feature of hydrogen's emission spectrum.
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Electromagnetic Spectrum
The electromagnetic spectrum encompasses all types of electromagnetic radiation, arranged by wavelength or frequency. It includes gamma rays, X-rays, ultraviolet light, visible light, infrared radiation, microwaves, and radio waves. The Lyman series specifically falls within the ultraviolet region of this spectrum.
Energy Level Transitions
Energy level transitions in an atom occur when an electron moves between different energy states. When an electron drops from a higher energy level to a lower one, it releases energy in the form of a photon. The energy of the emitted photon corresponds to the difference in energy between the two levels, determining the wavelength and thus the position in the electromagnetic spectrum.
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Related Practice
Textbook Question
The hydrogen atom can absorb light of wavelength 1094 nm. (a) In what region of the electromagnetic spectrum is this absorption found?
Textbook Question
One of the emission lines of the hydrogen atom has a wavelength of 94.974 nm. (b) Determine the initial and final values of n associated with this emission.
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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.
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Textbook Question
The visible emission lines observed by Balmer all involved nf = 2. (a) Which of the following is the best explanation of why the lines with nf = 3 are not observed in the visible portion of the spectrum: (i) Transitions to nf = 3 are not allowed to happen, (ii) transitions to nf = 3 emit photons in the infrared portion of the spectrum, (iii) transitions to nf = 3 emit photons in the ultraviolet portion of the spectrum, or (iv) transitions to nf = 3 emit photons that are at exactly the same wavelengths as those to nf = 2.
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Textbook Question
Consider a transition of the electron in the hydrogen atom from n = 8 to n = 3. (b) Will the light be absorbed or emitted?
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