University Physics with Modern Physics (14th Edition)
14th Edition
ISBN: 9780321973610
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 40, Problem 40.16E
(a)
To determine
For the particle in a box in the ground level, which value of
(b)
To determine
For the particle in a box in the ground level, which value of
(c)
To determine
whether the answers of part (a) and part (b) are consistent with the figure showing probability density of the particle at ground state.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
A particle is described by the wave function
[V5 cos 0 + sin(e + 4) + sin(0 – ø)],
2/3n
(a)
Express 4(0, 4) in terms of spherical harmonics
(b)
Calculate p and Lzµ. Is y an eigenstate of I? and L,?
(c)
Calculate Î44 and (L4)
If the measurement of Î, is carried out, find the probability of getting
the results 0,ħ and -ħ.
(d)
Consider a very simplistic model of atomic nucleus in 1D: a proton is completely localized
in a 1D box of width L = 1.00 × 10¬14m. In other words, the proton wavefunction outside
of the "nucleus" is zero. Note that L represents a typical nuclear radius.
(A) What are the energies of the ground and the first excited states? If the proton makes a
transition from the first excited state to the ground state, what is the angular frequency
of the emitted photon?
(B) What is the probability that the proton in its ground state (i.e., the lowest energy
state) is not found in the distance L/12 around each boundary of the box?
(C) Using the uncertainty principle, derive a minimum possible value on the momentum
uncertainty in the second state above the ground state.
(D) Compare your answer to the previous question (B) to probability distribution one would
obtain for a classical particle. First argue about how the probability distribution would
look for a classical object in its ground state. How…
The Einstein's model makes the assumption that a solid can be treated a set of N identical, independent
harmonic oscillators. Compute the heat capacity for such a system. Make the simplifying assumption that a single
harmonic oscillator is described by the quantized energy levels: E, = kħw, where k = 0,1, 2, ....
Chapter 40 Solutions
University Physics with Modern Physics (14th Edition)
Ch. 40.1 - Does a wave packet given by Eq. (40.19) represent...Ch. 40.2 - Prob. 40.2TYUCh. 40.3 - Prob. 40.3TYUCh. 40.4 - Prob. 40.4TYUCh. 40.5 - Prob. 40.5TYUCh. 40.6 - Prob. 40.6TYUCh. 40 - Prob. 40.1DQCh. 40 - Prob. 40.2DQCh. 40 - Prob. 40.3DQCh. 40 - Prob. 40.4DQ
Ch. 40 - If a panicle is in a stationary state, does that...Ch. 40 - Prob. 40.6DQCh. 40 - Prob. 40.7DQCh. 40 - Prob. 40.8DQCh. 40 - Prob. 40.9DQCh. 40 - Prob. 40.10DQCh. 40 - Prob. 40.11DQCh. 40 - Prob. 40.12DQCh. 40 - Prob. 40.13DQCh. 40 - Prob. 40.14DQCh. 40 - Prob. 40.15DQCh. 40 - Prob. 40.16DQCh. 40 - Prob. 40.17DQCh. 40 - Prob. 40.18DQCh. 40 - Prob. 40.19DQCh. 40 - Prob. 40.20DQCh. 40 - Prob. 40.21DQCh. 40 - Prob. 40.22DQCh. 40 - Prob. 40.23DQCh. 40 - Prob. 40.24DQCh. 40 - Prob. 40.25DQCh. 40 - Prob. 40.26DQCh. 40 - Prob. 40.27DQCh. 40 - Prob. 40.1ECh. 40 - Prob. 40.2ECh. 40 - Prob. 40.3ECh. 40 - Prob. 40.4ECh. 40 - Prob. 40.5ECh. 40 - Prob. 40.6ECh. 40 - Prob. 40.7ECh. 40 - Prob. 40.8ECh. 40 - Prob. 40.9ECh. 40 - Prob. 40.10ECh. 40 - Prob. 40.11ECh. 40 - Prob. 40.12ECh. 40 - Prob. 40.13ECh. 40 - Prob. 40.14ECh. 40 - Prob. 40.15ECh. 40 - Prob. 40.16ECh. 40 - Prob. 40.17ECh. 40 - Prob. 40.18ECh. 40 - Prob. 40.19ECh. 40 - Prob. 40.20ECh. 40 - Prob. 40.21ECh. 40 - Prob. 40.22ECh. 40 - Prob. 40.23ECh. 40 - Prob. 40.24ECh. 40 - Prob. 40.25ECh. 40 - Prob. 40.26ECh. 40 - Prob. 40.27ECh. 40 - Prob. 40.28ECh. 40 - Prob. 40.29ECh. 40 - Prob. 40.30ECh. 40 - Prob. 40.31ECh. 40 - Prob. 40.32ECh. 40 - Prob. 40.33ECh. 40 - Prob. 40.34ECh. 40 - Prob. 40.35ECh. 40 - Prob. 40.36ECh. 40 - Prob. 40.37ECh. 40 - Prob. 40.38ECh. 40 - Prob. 40.39ECh. 40 - Prob. 40.40ECh. 40 - Prob. 40.41ECh. 40 - Prob. 40.42PCh. 40 - Prob. 40.43PCh. 40 - Prob. 40.44PCh. 40 - Prob. 40.45PCh. 40 - Prob. 40.46PCh. 40 - Prob. 40.47PCh. 40 - Prob. 40.48PCh. 40 - Prob. 40.49PCh. 40 - Prob. 40.50PCh. 40 - Prob. 40.51PCh. 40 - Prob. 40.52PCh. 40 - Prob. 40.53PCh. 40 - Prob. 40.54PCh. 40 - Prob. 40.55PCh. 40 - Prob. 40.56PCh. 40 - Prob. 40.57PCh. 40 - Prob. 40.58PCh. 40 - Prob. 40.59PCh. 40 - Prob. 40.60PCh. 40 - Prob. 40.61PCh. 40 - Prob. 40.62PCh. 40 - Prob. 40.63PCh. 40 - Prob. 40.64CPCh. 40 - Prob. 40.65CPCh. 40 - Prob. 40.66CPCh. 40 - Prob. 40.67PPCh. 40 - Prob. 40.68PPCh. 40 - Prob. 40.69PPCh. 40 - Prob. 40.70PP
Knowledge Booster
Similar questions
- A particle in a box is in the ground level. What is the probability of finding the particle in the right half of the box? (Refer to Fig. , but don’t evaluate an integral.) Is the answer the same if the particle is in an excited level? Explain.arrow_forwardA proton is confined in box whose width is d = 750 nm. It is in the n = 3 energy state. What is the probability that the proton will be found within a distance of d/n from one of the walls? [Hint: the average value sin2x over one or more of its cycles is 1/2.] Include a sketch of U(x) and ?(x).arrow_forward∆E ∆t ≥ ħTime is a parameter, not an observable. ∆t is some timescale over which the expectation value of an operator changes. For example, an electron's angular momentum in a hydrogen atom decays from 2p to 1s. These decays are relativistic, however the uncertainty principle is still valid, and we can use it to estimate uncertainties. ∆E doesn't change in time, so when an excited state decays to the ground state (infinite lifetime, so no energy uncertainty), the energy uncertainty has to go somewhere. Usually, it’s in the frequency of a photon giving a width (through E = hν) to the transition line in an spectroscopy experiment. The linewidth of the 2p state in 9Be+ is 19.4 MHz. What is its lifetime? (Note: in the relativistic atom–photon system, the Hamiltonian is independent of time and both energy and its uncertainty are conserved.)arrow_forward
- We are going to use Heisenberg's uncertainty principle to estimate the ground- state energy of hydrogen. In our model, the electron is confined in a one- dimensional well with a length about the size of hydrogen, so that Ax = 0.0529 nm. Estimate Ap, and then assume that the ground-state energy is roughly Ap2/2me. (Give your answer in Joules or electron-volts.)arrow_forward∆E ∆t ≥ ħTime is a parameter, not an observable. ∆t is some timescale over which the expectation value of an operator changes. For example, an electron's angular momentum in a hydrogen atom decays from 2p to 1s. These decays are relativistic, however the uncertainty principle is still valid, and we can use it to estimate uncertainties. The lifetime of hydrogen in the 2p state to decay to the Is ground state is 1.6 x 10-9 s. Estimate the uncertainty ∆E in energy of this excited state. What is the corresponding linewidth in angstroms?arrow_forwardThe eigenfunction for OHS for n=1 is of the form Vi(x) = -「网2 ep with value = "ħw mo and energy E1 = a. Write the form of the function as a solution of the Schrodinger equation for this OHS (v(x,t) b. Draw the wave function and energy levels of this OHS until n = 4. %3Darrow_forward
- 1arrow_forwardChapter 38, Problem 071 For the arrangement of Figure (a) and Figure (b), electrons in the incident beam in region 1 have energy E has a height of U1 = 823 ev and the potential step = 617 ev. What is the angular wave number in (a) region 1 and (b) region 2? (c) What is the reflection coefficient? (d) If the incident beam sends 5.29 x 105 electrons against the potential step, approximately how many will be reflected? V= 0 V< 0 x = 0 region 1 region 2 (a) Energy --E- Electron (b)arrow_forwardDetermine the probability of an electron in the region of x = 0.490L and 0.510L in a box of length L in the energy level n = 1.arrow_forward
- An electron has a wave function Y(x) = Ce-kl/xo %3D where x0 is a constant and C = 1//x0 is the normalization constant. In this case, get the expressions for (x) And Ax in terms of x0. Also calculate the probability that the electron is found within the standard deviation of its average position, that is, in the range (x) –Ax a (x) + Ax, show that this is independent of x0.arrow_forwardExpress the complex number z1 = (√(3) + i)/2 in the form rei Φ. What about z2 = (1 + √(3i))/2? If these complex numbers are the probability amplitudes for photons to be detected, what is the probability in each case? (Hint: See attatched image for more on finding probability amplitudes)arrow_forwardhelp with modern physics questionarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON