Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 10, Problem 10.66E
Interpretation Introduction
Interpretation:
The value of
Concept introduction:
In
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
(a) For a particle in the stationary state n of a one dimensional box of length a, find the probability that the particle is in the region 0xa/4.(b) Calculate this probability for n=1,2, and 3.
For a particle in the stationary state n of a one dimensional box of length a, find the probability that the particle is in the region 0 xa/4. (b) Calculate this probability for n = 1, 2, and 3
Calculate the expectation values of x and x2 for a particle in the state with n = 1 in a one-dimensional square-well potential.
Chapter 10 Solutions
Physical Chemistry
Ch. 10 - State the postulates of quantum mechanics...Ch. 10 - Prob. 10.2ECh. 10 - State whether the following functions are...Ch. 10 - State whether the following functions are...Ch. 10 - Prob. 10.5ECh. 10 - Prob. 10.6ECh. 10 - Evaluate the operations in parts a, b, and f in...Ch. 10 - The following operators and functions are defined:...Ch. 10 - Prob. 10.9ECh. 10 - Indicate which of these expressions yield...
Ch. 10 - Indicate which of these expressions yield an...Ch. 10 - Why is multiplying a function by a constant...Ch. 10 - Prob. 10.13ECh. 10 - Using the original definition of the momentum...Ch. 10 - Under what conditions would the operator described...Ch. 10 - A particle on a ring has a wavefunction =12eim...Ch. 10 - Calculate the uncertainty in position, x, of a...Ch. 10 - For an atom of mercury, an electron in the 1s...Ch. 10 - Classically, a hydrogen atom behaves as if it were...Ch. 10 - The largest known atom, francium, has an atomic...Ch. 10 - How is the Bohr theory of the hydrogen atom...Ch. 10 - Though not strictly equivalent, there is a similar...Ch. 10 - The uncertainty principle is related to the order...Ch. 10 - Prob. 10.24ECh. 10 - Prob. 10.25ECh. 10 - For a particle in a state having the wavefunction...Ch. 10 - Prob. 10.27ECh. 10 - A particle on a ring has a wavefunction =eim,...Ch. 10 - Prob. 10.29ECh. 10 - Prob. 10.30ECh. 10 - Prob. 10.31ECh. 10 - Normalize the following wavefunctions over the...Ch. 10 - Prob. 10.33ECh. 10 - Prob. 10.34ECh. 10 - For an unbound or free particle having mass m in...Ch. 10 - Prob. 10.36ECh. 10 - Prob. 10.37ECh. 10 - Prob. 10.38ECh. 10 - Evaluate the expression for the total energies for...Ch. 10 - Prob. 10.40ECh. 10 - Verify that the following wavefunctions are indeed...Ch. 10 - In exercise 10.41a, the wavefunction is not...Ch. 10 - Prob. 10.43ECh. 10 - Prob. 10.44ECh. 10 - Explain why n=0 is not allowed for a...Ch. 10 - Prob. 10.46ECh. 10 - Prob. 10.47ECh. 10 - Prob. 10.48ECh. 10 - Carotenes are molecules with alternating CC and...Ch. 10 - The electronic spectrum of the molecule butadiene,...Ch. 10 - Prob. 10.51ECh. 10 - Prob. 10.52ECh. 10 - Show that the normalization constants for the...Ch. 10 - Prob. 10.54ECh. 10 - Prob. 10.55ECh. 10 - An official baseball has a mass of 145g. a...Ch. 10 - Is the uncertainty principle consistent with our...Ch. 10 - Prob. 10.58ECh. 10 - Prob. 10.59ECh. 10 - Instead of x=0 to a, assume that the limits on the...Ch. 10 - In a plot of ||2, the maximum maxima in the plot...Ch. 10 - Prob. 10.62ECh. 10 - Prob. 10.63ECh. 10 - The average value of radius in a circular system,...Ch. 10 - Prob. 10.65ECh. 10 - Prob. 10.66ECh. 10 - Prob. 10.67ECh. 10 - Prob. 10.68ECh. 10 - Prob. 10.69ECh. 10 - Assume that for a particle on a ring the operator...Ch. 10 - Mathematically, the uncertainty A in some...Ch. 10 - Prob. 10.72ECh. 10 - Prob. 10.73ECh. 10 - Verify that the wavefunctions in equation 10.20...Ch. 10 - An electron is confined to a box of dimensions...Ch. 10 - a What is the ratio of energy levels having the...Ch. 10 - Consider a one-dimensional particle-in-a-box and a...Ch. 10 - Prob. 10.78ECh. 10 - Prob. 10.79ECh. 10 - Prob. 10.80ECh. 10 - Prob. 10.81ECh. 10 - What are x,y, and z for 111 of a 3-D...Ch. 10 - Prob. 10.83ECh. 10 - Prob. 10.84ECh. 10 - Prob. 10.85ECh. 10 - Prob. 10.86ECh. 10 - Prob. 10.87ECh. 10 - Prob. 10.88ECh. 10 - Substitute (x,t)=eiEt/(x) into the time-dependent...Ch. 10 - Write (x,t)=eiEt/(x) in terms of sine and cosine,...Ch. 10 - Prob. 10.91ECh. 10 - Prob. 10.92ECh. 10 - Prob. 10.93ECh. 10 - Prob. 10.95E
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.Similar questions
- What is the physical explanation of the difference between a particle having the 3-D rotational wavefunction 3,2 and an identical particle having the wavefunction 3,2?arrow_forwardFor a particle in a state having the wavefunction =2asinxa in the range x=0toa, what is the probability that the particle exists in the following intervals? a x=0to0.02ab x=0.24ato0.26a c x=0.49ato0.51ad x=0.74ato0.76a e x=0.98ato1.00a Plot the probabilities versus x. What does your plot illustrate about the probability?arrow_forwardDraw, label, and explain the functions of the parts of a spectroscope.arrow_forward
- Indicate which of these expressions yield an eigenvalue equation, and if so indicate the eigenvalue. a ddxcos4xb d2dx2cos4x c px(sin2x3)d x(2asin2xa) e 3(4lnx2), where 3=3f ddsincos g d2d2sincosh ddtanarrow_forwardFor the system described in Exercise E7C.8(a), evaluate the expectation value of the angular momentum represented by the operator(ħ/i)d/dϕ for the case ml = +1, and then for the general case of integer ml.arrow_forwardFor a particle in a box of length L and in the state with n = 3, at what positions is the probability density a maximum? At what positions is the probability density zero?arrow_forward
- Find an expression for the value of n of a particle of mass m in a one-dimensional box of length L such that the energy of the level is equal to the mean energy of thermal motion (1/2kT). Calculate the value of n for the case of an argon atom in a box of length 0.1 cm at 298 K.arrow_forwardConstruct the potential energy operator of a particle with potential energy V(x)=1/2kfx2, where kf is a constantarrow_forwardConsider a particle of mass m confined to a one-dimensional box of length L and in a state with normalized wavefunction ψn. (a) Without evaluating any integrals, explain why ⟨x⟩ = L/2. (b) Without evaluating any integrals, explain why ⟨px⟩ = 0. (c) Derive an expression for ⟨x2⟩ (the necessary integrals will be found in the Resource section). (d) For a particle in a box the energy is given by En = n2h2/8mL2 and, because the potential energy is zero, all of this energy is kinetic. Use this observation and, without evaluating any integrals, explain why <p2x> = n2h2/4L2.arrow_forward
- By considering the integral ∫02π ψ*ml ψml dϕ, where ml≠m'l, confirm that wavefunctions for a particle in a ring with different values of the quantum number ml are mutually orthogonal.arrow_forwardFor a particle on a ring, how many nodes are there in the real part, and in the imaginary part of the wavefunction for (i) ml = +1 and (ii) ml = +2? In both cases, find the values of ϕ at which any nodes occur.arrow_forwardConsider a particle in a cubic box. What is the degeneracy (1,2,3, etc) of the level that has an energy a.) two times that of the lowest level? b.) Three times that of the lowest level? c.) four times that of the lowest level?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Introductory Chemistry: A FoundationChemistryISBN:9781337399425Author:Steven S. Zumdahl, Donald J. DeCostePublisher:Cengage LearningPrinciples of Instrumental AnalysisChemistryISBN:9781305577213Author:Douglas A. Skoog, F. James Holler, Stanley R. CrouchPublisher:Cengage Learning
Physical Chemistry
Chemistry
ISBN:9781133958437
Author:Ball, David W. (david Warren), BAER, Tomas
Publisher:Wadsworth Cengage Learning,
Introductory Chemistry: A Foundation
Chemistry
ISBN:9781337399425
Author:Steven S. Zumdahl, Donald J. DeCoste
Publisher:Cengage Learning
Principles of Instrumental Analysis
Chemistry
ISBN:9781305577213
Author:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:Cengage Learning