Domanda del libro di testo
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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TOC.tableOfContents
- Ch.1 - Introduction: Matter, Energy, and Measurement177
- Ch.2 - Atoms, Molecules, and Ions231
- Ch.3 - Chemical Reactions and Reaction Stoichiometry216
- Ch.4 - Reactions in Aqueous Solution189
- Ch.5 - Thermochemistry175
- Ch.6 - Electronic Structure of Atoms168
- Ch.7 - Periodic Properties of the Elements150
- Ch.8 - Basic Concepts of Chemical Bonding177
- Ch.9 - Molecular Geometry and Bonding Theories200
- Ch.10 - Gases179
- Ch.11 - Liquids and Intermolecular Forces113
- Ch.12 - Solids and Modern Materials154
- Ch.13 - Properties of Solutions157
- Ch.14 - Chemical Kinetics199
- Ch.15 - Chemical Equilibrium128
- Ch.16 - Acid-Base Equilibria164
- Ch.17 - Additional Aspects of Aqueous Equilibria163
- Ch.18 - Chemistry of the Environment105
- Ch.19 - Chemical Thermodynamics164
- Ch.20 - Electrochemistry171
- Ch.21 - Nuclear Chemistry122
- Ch.22 - Chemistry of the Nonmetals82
- Ch.23 - Transition Metals and Coordination Chemistry79
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry16
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Non è quello che usi tu?Cambia libro di testo
Capitolo 6, Problema 42b
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.
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Identify the formula to calculate the wavelength of the emission lines in the hydrogen spectrum, which is given by the Rydberg formula: \( \frac{1}{\lambda} = R_H \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right) \), where \( \lambda \) is the wavelength, \( R_H \) is the Rydberg constant (approximately 1.097 x 10^7 m^-1), \( n_f \) is the final energy level, and \( n_i \) is the initial energy level.
Set \( n_f = 1 \) for the Lyman series as given in the problem statement.
Calculate the wavelength for the first line in the series where \( n_i = 2 \). Plug these values into the Rydberg formula and solve for \( \lambda \).
Repeat the calculation for the second line in the series where \( n_i = 3 \).
Repeat the calculation for the third line in the series where \( n_i = 4 \).
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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 (ni) to the lowest energy level (nf = 1). These transitions result in the emission of ultraviolet light, and the wavelengths of these lines can be calculated using the Rydberg formula.
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02:02
Activity Series Chart
Rydberg Formula
The Rydberg formula is an equation used to predict the wavelengths of spectral lines in hydrogen and other hydrogen-like atoms. It is expressed as 1/λ = R_H (1/nf^2 - 1/ni^2), where R_H is the Rydberg constant, λ is the wavelength, nf is the final energy level, and ni is the initial energy level. This formula is essential for calculating the wavelengths of the Lyman series.
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02:26Skeletal Formula
Energy Levels in Hydrogen Atom
In a hydrogen atom, electrons occupy discrete energy levels, which are quantized. The energy levels are defined by the principal quantum number n, where n = 1 is the ground state. When an electron transitions between these levels, energy is emitted or absorbed in the form of photons, with the energy difference corresponding to the wavelength of the emitted light.
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01:22Hydrogenation Reactions
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Domanda del libro di testo
The hydrogen atom can absorb light of wavelength 1094 nm. (a) In what region of the electromagnetic spectrum is this absorption found?
Domanda del libro di testo
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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Domanda del libro di testo
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.
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Domanda del libro di testo
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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Domanda del libro di testo
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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