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. (b) What is the value of the angular momentum quantum number, l?
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Ch.6 - Electronic Structure of Atoms
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970
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TOC.tableOfContents
- Ch.1 - Introduction: Matter, Energy, and Measurement146
- Ch.2 - Atoms, Molecules, and Ions200
- Ch.3 - Chemical Reactions and Reaction Stoichiometry176
- Ch.4 - Reactions in Aqueous Solution155
- Ch.5 - Thermochemistry126
- Ch.6 - Electronic Structure of Atoms131
- Ch.7 - Periodic Properties of the Elements126
- Ch.8 - Basic Concepts of Chemical Bonding123
- Ch.9 - Molecular Geometry and Bonding Theories143
- Ch.10 - Gases147
- Ch.11 - Liquids and Intermolecular Forces91
- Ch.12 - Solids and Modern Materials122
- Ch.13 - Properties of Solutions126
- Ch.14 - Chemical Kinetics174
- Ch.15 - Chemical Equilibrium101
- Ch.16 - Acid-Base Equilibria139
- Ch.17 - Additional Aspects of Aqueous Equilibria146
- Ch.18 - Chemistry of the Environment72
- Ch.19 - Chemical Thermodynamics129
- Ch.20 - Electrochemistry142
- Ch.21 - Nuclear Chemistry101
- Ch.22 - Chemistry of the Nonmetals68
- Ch.23 - Transition Metals and Coordination Chemistry66
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry10
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Non è quello che usi tu?Cambia libro di testo
Capitolo 6, Problema 8b
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?
Guida verificata passo dopo passo1
Identify the wave function given: \( \psi(x) = \sin(x) \) for \( x \) ranging from 0 to 2\(\pi\).
Recall that the probability density function is given by the square of the wave function: \( |\psi(x)|^2 = (\sin(x))^2 \).
Determine the values of \( x \) where \( (\sin(x))^2 \) is maximized. Since \( \sin(x) \) ranges from -1 to 1, the maximum value of \( (\sin(x))^2 \) is 1.
Find the values of \( x \) where \( \sin(x) = \pm 1 \). These occur at \( x = \frac{\pi}{2} \) and \( x = \frac{3\pi}{2} \) within the given range.
Conclude that the greatest probability of finding the electron is at \( x = \frac{\pi}{2} \) and \( x = \frac{3\pi}{2} \).
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Wave Function
The wave function is a mathematical description of the quantum state of a system, representing the probability amplitude of finding a particle in a given position. In this case, the wave function is given as sin(x), which describes the behavior of the electron in a one-dimensional system. The square of the wave function's magnitude gives the probability density, indicating where the electron is likely to be found.
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03:37
Logarithmic Functions
Probability Density
Probability density is derived from the wave function and indicates the likelihood of finding a particle in a specific region of space. For a wave function ψ(x), the probability density is given by |ψ(x)|². In the context of the provided wave function sin(x), the peaks of the graph correspond to higher probabilities of locating the electron, while the nodes (where the function crosses zero) indicate positions where the electron cannot be found.
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01:56Density Concepts
Nodes and Antinodes
In wave mechanics, nodes are points where the wave function is zero, resulting in zero probability of finding the particle, while antinodes are points where the wave function reaches its maximum value, indicating the highest probability of finding the particle. In the graph of sin(x), the peaks represent antinodes, where the electron is most likely to be found, while the points where the function crosses the x-axis are nodes, indicating locations of zero probability.
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01:04Radial and Angular Nodes
Pratica correlata
Domanda del libro di testo
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
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?
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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. (a) Three electromagnetic waves, all drawn on the same scale, are also shown. Each corresponds to one of the transitions. Which electromagnetic wave (i), (ii), or (iii), is associated with electronic transition C?
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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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