Domanda del libro di testo
Write the electron configurations for the following ions, and
determine which have noble-gas configurations:
(a) Ti2+
(b) Br-
(c) Mg2+
(d) Po2-
(e) Pt2+
(f) V3+
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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 45
Order the following transitions in the hydrogen atom from smallest to largest frequency of light absorbed: n = 3 to n = 7, n = 4 to n = 8, n = 2 to n = 5, and n = 1 to n = 3.
Guida verificata passo dopo passo1
Identify the initial and final energy levels for each transition. For example, for the transition n = 3 to n = 7, the initial level (ni) is 3 and the final level (nf) is 7.
Use the formula for the frequency of light absorbed during a transition in a hydrogen atom, which is derived from the energy difference between the two levels: \( \Delta E = E_f - E_i \) where \( E_n = -\frac{13.6 \text{ eV}}{n^2} \) for a hydrogen atom.
Calculate the energy difference for each transition using the formula: \( \Delta E = -13.6 \text{ eV} \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right) \).
Convert the energy difference to frequency using the relation \( \Delta E = h \nu \), where \( h \) is Planck's constant. Solve for \( \nu \) to find the frequency: \( \nu = \frac{\Delta E}{h} \).
Compare the frequencies calculated for each transition to determine the order from smallest to largest frequency.
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Concetti chiave
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Energy Levels in Hydrogen Atom
In a hydrogen atom, electrons occupy discrete energy levels, denoted by quantum numbers (n). The energy associated with each level increases with n, meaning that transitions between levels involve the absorption or emission of energy in the form of light. The difference in energy between two levels determines the frequency of the light absorbed or emitted during a transition.
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01:22
Hydrogenation Reactions
Rydberg Formula
The Rydberg formula provides a way to calculate the wavelengths (and thus frequencies) of light emitted or absorbed during electron transitions in hydrogen. It states that the frequency of light (ν) is proportional to the difference in the inverse squares of the principal quantum numbers (n) of the initial and final states. This relationship allows for the determination of the frequency based on the specific transitions being analyzed.
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02:26Skeletal Formula
Frequency and Energy Relationship
The frequency of light is directly related to its energy through the equation E = hν, where E is energy, h is Planck's constant, and ν is frequency. Higher energy transitions correspond to higher frequencies of light. Therefore, by calculating the energy differences for each transition, one can rank them from smallest to largest frequency absorbed.
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00:31Frequency-Wavelength Relationship
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Domanda del libro di testo
The hydrogen atom can absorb light of wavelength 1094 nm. (b) Determine the final value of n associated with this absorption.
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