Domanda del libro di testo
The series of emission lines of the hydrogen atom for which nf = 3 is called the Paschen series. (b) Calculate the wavelengths of the first three lines in the Paschen series—those for which ni = 4, 5, and 6.
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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 89d
Consider a transition in which the electron of a hydrogen atom is excited from n = 1 to n = ∞. (d) How are the results of parts (b) and (c) related to the plot shown in Exercise 6.88?
Guida verificata passo dopo passo1
Identify the initial and final energy levels of the electron transition in the hydrogen atom (n = 1 to n = ?).
Use the Rydberg formula to calculate the energy difference between these levels: \( \Delta E = -R_H \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right) \), where \( R_H \) is the Rydberg constant, \( n_f \) is the final energy level, and \( n_i \) is the initial energy level.
Relate the energy difference to the frequency of the emitted or absorbed photon using the equation \( \Delta E = h \nu \), where \( h \) is Planck's constant and \( \nu \) is the frequency.
Analyze the provided graph, which shows the relationship between electron kinetic energy and frequency. Note that the kinetic energy of the electron is zero until a threshold frequency \( \nu_0 \) is reached, after which it increases linearly with frequency.
Compare the calculated energy difference and frequency from the Rydberg formula to the threshold frequency \( \nu_0 \) and the slope of the line in the graph to understand how the energy levels and transitions relate to the kinetic energy of the electron.
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Quantum Energy Levels
In quantum mechanics, electrons in an atom occupy discrete energy levels, denoted by quantum numbers (n). For hydrogen, these levels are quantized, meaning an electron can only exist in specific states. The transition from a lower level (n=1) to a higher level (n=2, 3, etc.) involves the absorption of energy, typically in the form of a photon, which corresponds to the energy difference between these levels.
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02:55
Principal Quantum Number
Photon Energy and Frequency
The energy of a photon is directly related to its frequency through the equation E = hν, where E is energy, h is Planck's constant, and ν is frequency. When an electron transitions between energy levels, it absorbs or emits a photon with energy equal to the difference between the two levels. This relationship is crucial for understanding how the frequency of light corresponds to specific electronic transitions in atoms.
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01:40Photon Energy Formulas
Kinetic Energy and Electron Transitions
The kinetic energy of an electron in an atom can change during electronic transitions. When an electron absorbs energy and moves to a higher energy level, it may also gain kinetic energy, which is reflected in the graph. The plot illustrates how the kinetic energy of the electron increases with frequency, indicating that only photons with sufficient energy (above a threshold frequency, ν₀) can cause transitions that result in increased kinetic energy.
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00:34Kinetic & Potential Energy
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The human retina has three types of receptor cones, each sensitive to a different range of wavelengths of visible light, as shown in this figure (the colors are merely to differentiate the three curves from one another; they do not indicate the actual colors represented by each curve):
(c) Explain why the sky appears blue even though all wavelengths of solar light are scattered by the atmosphere.
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Domanda del libro di testo
Consider a transition in which the electron of a hydrogen atom is excited from n = 1 to n = ∞. (a) What is the end result of this transition?
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Domanda del libro di testo
The series of emission lines of the hydrogen atom for which nf = 3 is called the Paschen series. (a) Determine the region of the electromagnetic spectrum in which the lines of the Paschen series are observed.
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Domanda del libro di testo
Consider a transition in which the electron of a hydrogen atom is excited from n = 1 to n = ∞. (b) What is the wavelength of light that must be absorbed to accomplish this process?
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Domanda del libro di testo
Consider a transition in which the electron of a hydrogen atom is excited from n = 1 to n = ∞. (c) What will occur if light with a shorter wavelength than that in part (b) is used to excite the hydrogen atom?
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