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The accompanying drawing shows a contour plot for a dyz orbital. Consider the quantum numbers that could potentially correspond to this orbital. (b) What is the value of the angular momentum quantum number, l?
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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 9a
The contour representation of one of the orbitals for the n = 3 shell of a hydrogen atom is shown here. (a) What is the quantum number l for this orbital?
Guida verificata passo dopo passo1
Identify the shape of the orbital from the image. The image shows a dumbbell-shaped orbital.
Recall that the dumbbell shape corresponds to a p-orbital.
Understand that p-orbitals have an angular momentum quantum number (l) of 1.
Since the principal quantum number (n) is given as 3, the possible values for the angular momentum quantum number (l) are 0, 1, and 2.
Conclude that for a p-orbital in the n=3 shell, the quantum number l is 1.
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Quantum Numbers
Quantum numbers are a set of numerical values that describe the unique quantum state of an electron in an atom. The four quantum numbers include the principal quantum number (n), which indicates the energy level; the angular momentum quantum number (l), which describes the shape of the orbital; the magnetic quantum number (m_l), which specifies the orientation of the orbital; and the spin quantum number (m_s), which indicates the spin direction of the electron.
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02:55
Principal Quantum Number
Angular Momentum Quantum Number (l)
The angular momentum quantum number (l) determines the shape of an electron's orbital and can take on integer values from 0 to n-1, where n is the principal quantum number. For example, if n=3, l can be 0, 1, or 2, corresponding to s, p, and d orbitals, respectively. The value of l also influences the energy and spatial distribution of the electron within the atom.
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00:40Angular Momentum Quantum Number
Orbital Shapes
Orbitals are regions in an atom where there is a high probability of finding electrons. The shape of an orbital is determined by the angular momentum quantum number (l). For instance, an l value of 0 corresponds to a spherical s orbital, l=1 corresponds to a dumbbell-shaped p orbital, and l=2 corresponds to more complex d orbitals. The image provided depicts a p orbital, which is indicative of l=1.
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01:47Quantum Numbers and Orbital Shape Example
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Consider the three electronic transitions in a hydrogen atom shown here, labeled A, B, and C. (c) Calculate the wavelength of the photon emitted for each transition. Do any of these transitions lead to the emission of visible light? If so which one(s)?
Calculate the wavelength of the photon emitted for transition B.
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Domanda del libro di testo
Consider the three electronic transitions in a hydrogen atom shown here, labeled A, B, and C. (b) Calculate the energy of the photon emitted for each transition.
Calculate the energy of the photon emitted for transition C.
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Domanda del libro di testo
Consider a fictitious one-dimensional system with one electron. The wave function for the electron, drawn below, is c1x2 = sin x from x = 0 to x = 2p. (b) At what value or values of x will there be the greatest probability of finding the electron?
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Domanda del libro di testo
The accompanying drawing shows a contour plot for a dyz orbital. Consider the quantum numbers that could potentially correspond to this orbital. (c) What is the largest possible value of the magnetic quantum number, ml?
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Domanda del libro di testo
The contour representation of one of the orbitals for the n = 3 shell of a hydrogen atom is shown here. (c) In which of the following ways would you modify this sketch if the value of the magnetic quantum number, ml, were to change? (i) It would be drawn larger, (ii) the number of lobes would change, (iii) the lobes of the orbital would point in a different direction, (iv) there would be no change in the sketch.
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