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 44b
The hydrogen atom can absorb light of wavelength 1094 nm. (b) Determine the final value of n associated with this absorption.
Guida verificata passo dopo passo1
Identify the formula to use: The Rydberg formula for hydrogen absorption is \( \frac{1}{\lambda} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \), where \( \lambda \) is the wavelength, \( R_H \) is the Rydberg constant (1.097 \(\times\) 10^7 \(\text{ m}\)^{-1}), \( n_1 \) is the initial energy level, and \( n_2 \) is the final energy level.
Convert the wavelength from nanometers to meters: Since 1 nm = 1 \(\times\) 10^{-9} m, convert 1094 nm to meters.
Assume the initial energy level \( n_1 \) is 1, as the problem does not specify it, and this is a common assumption for absorption from the ground state.
Rearrange the Rydberg formula to solve for \( n_2 \): \( n_2 = \sqrt{\frac{1}{\frac{1}{n_1^2} - \frac{\lambda}{R_H}}} \).
Substitute the known values into the equation: Use the converted wavelength and the Rydberg constant to calculate \( n_2 \).
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Energy of Photons
The energy of a photon is directly related to its wavelength, described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. For the hydrogen atom, when it absorbs a photon, the energy from the photon is used to excite an electron to a higher energy level.
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Percorso guidato
01:40
Photon Energy Formulas
Quantum Energy Levels
In a hydrogen atom, electrons occupy discrete energy levels, denoted by the principal quantum number n. The energy associated with each level can be calculated using the formula E_n = -13.6 eV/n². When a photon is absorbed, the electron transitions from a lower energy level (n_initial) to a higher one (n_final), and the difference in energy corresponds to the energy of the absorbed photon.
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Percorso guidato
02:55Principal Quantum Number
Balmer and Rydberg Formulas
The Rydberg formula allows for the calculation of the wavelengths of spectral lines in hydrogen and is given by 1/λ = R_H(1/n_final² - 1/n_initial²). This formula is essential for determining the final energy level (n_final) after absorption, as it relates the wavelength of light absorbed to the transition between quantum states of the hydrogen atom.
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Percorso guidato
01:00Balmer Series Example
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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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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?
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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
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.
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