College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 28, Problem 30P
(a)
To determine
The expression for the linear momentum of the particle which is quantized.
(b)
To determine
The expression for the allowed state of the particle which is quantized.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Using the concept of standing waves, de Broglie was able to derive Bohr’s stationary orbit postulate. He assumed a confined electron could exist only in states where its de Broglie waves form standing wave patterns. Consider a particle confined in a box of length L to be equivalent to a string of length L and fixed at both ends. Apply de Broglie’s concept to show that (a) the linear momentum of this particle is quantized with p = mv = nh/2L and (b) the allowed states correspond to particle energies of En = n 2E 0, where E 0 = h 2/(8mL2)
An electron is confined between two perfectly reflecting walls separated by the distance 12 x 10-11m. Use the Heisenberg uncertainty relation to estimate the lowest energy that the particle can have (in eV).
Show that the wave function ψ = Ae i(i-ωt) is a solution to the Schrödinger equation (as shown), where k = 2π/λ and U = 0.
Chapter 28 Solutions
College Physics
Ch. 28.3 - Prob. 28.1QQCh. 28.4 - Prob. 28.2QQCh. 28.5 - Prob. 28.3QQCh. 28 - Prob. 1CQCh. 28 - Prob. 2CQCh. 28 - Prob. 3CQCh. 28 - Prob. 4CQCh. 28 - Prob. 5CQCh. 28 - Prob. 6CQCh. 28 - Prob. 7CQ
Ch. 28 - Prob. 8CQCh. 28 - Prob. 9CQCh. 28 - Prob. 10CQCh. 28 - Prob. 11CQCh. 28 - Prob. 12CQCh. 28 - Prob. 13CQCh. 28 - Prob. 14CQCh. 28 - Prob. 15CQCh. 28 - Prob. 1PCh. 28 - Prob. 2PCh. 28 - Prob. 3PCh. 28 - Prob. 4PCh. 28 - Prob. 5PCh. 28 - Prob. 6PCh. 28 - Prob. 7PCh. 28 - Prob. 8PCh. 28 - Prob. 9PCh. 28 - Prob. 10PCh. 28 - Prob. 11PCh. 28 - Prob. 12PCh. 28 - Prob. 13PCh. 28 - Prob. 14PCh. 28 - Prob. 15PCh. 28 - Prob. 16PCh. 28 - Prob. 17PCh. 28 - Prob. 18PCh. 28 - Prob. 19PCh. 28 - Prob. 20PCh. 28 - Prob. 21PCh. 28 - Prob. 22PCh. 28 - Prob. 23PCh. 28 - Prob. 24PCh. 28 - Prob. 25PCh. 28 - Prob. 26PCh. 28 - Prob. 27PCh. 28 - Prob. 28PCh. 28 - Prob. 29PCh. 28 - Prob. 30PCh. 28 - Prob. 31PCh. 28 - Prob. 32PCh. 28 - Prob. 33PCh. 28 - Prob. 34PCh. 28 - Prob. 35PCh. 28 - Prob. 36PCh. 28 - Prob. 37PCh. 28 - Prob. 38PCh. 28 - Prob. 39PCh. 28 - Prob. 40PCh. 28 - Prob. 41PCh. 28 - Prob. 42PCh. 28 - Prob. 43PCh. 28 - Prob. 44PCh. 28 - Prob. 45PCh. 28 - Prob. 46APCh. 28 - Prob. 47APCh. 28 - Prob. 48APCh. 28 - Prob. 49APCh. 28 - Prob. 50APCh. 28 - Prob. 51APCh. 28 - Prob. 52APCh. 28 - Prob. 53APCh. 28 - Prob. 54AP
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- An electron is moving past the square well shown in Fig. . The electron has energy E = 3U0 . What is the ratio of the de Broglie wavelength of the electron in the region x 7 L to the wavelength for 0 6 x 6 L?arrow_forwardWhat do you understand by the wave-particle duality?Estimate the de Broglie wavelength of an electron emitted by thermionic emission into a vacuum from a hot cathode an accelerated by a potential difference of 30.0kV.arrow_forwardFrom the de Broglie relationships, a free particle has associated with it a frequency f = E/h and a wavelength \ = h/p. Determine for what value of a the time-dependent wave function V (x, t) = A cos a( - ft) + i sin a(- ft) is a solution to the time-dependent Schrodinger equation for a free particle.arrow_forward
- An electron has a wavefunction ψ(x)=Ce-|x|/x0 where x0 is a constant and C=1/√x0 for normalization. For this case, obtain expressions for a. ⟨x⟩ and Δx in terms of x0. b. Also calculate the probability that the electron will be found within a standard deviation of its average position, that is, in the range ⟨x⟩-∆x to ⟨x⟩+∆x, and show that this is independent of x0.arrow_forwardConsider a one-dimensional square potential well with a width of L and depth Vo. An electron is confined within this potential well. a) Calculate the energy levels of the electron in terms of L and Vo. b) Determine the wavelength of the electron associated with its lowest energy state (n=1). c) If the potential well has the width of L=5nm and Vo=10eV, calculate the energy of the electron in its lowest energy state.arrow_forwardWhat is the value N so that ψ(x) = N/(a2 + x2) can give rise to a valid probability density?arrow_forward
- Show that normalizing the particle-in-a-box wave function ψ_n (x)=A sin(nπx/L) gives A=√(2/L).arrow_forwardAn electron is moving past the square barrier shown in Fig. , but the energy of the electron is greater than the barrier height. If E = 2U0 , what is the ratio of the de Broglie wavelength of the electron in the region x 7 L to the wavelength for 0 6 x 6 L?arrow_forwardConsider 1D particle in a box and it’s given normalized wave function Psi = Nsin(bx) where v(x) = 0 outside the box and v(x) = cos(pix/L) inside the box from x = 0 to x = 1. (a) show that the wave function is a valid solution to the Schrödinger equation and what value of b makes it valid? (b) derive the eigenvalue expressionarrow_forward
- We have discovered that an electron’s orbit must contain an integer number of de Broglie wavelengths. Explain why, under ordinary conditions, this makes it impossible for electrons to spiral in to merge with the positively charged nucleus.arrow_forwardConsider a singly charged Helium nucleus (He+). Argue that the Bohr model will work in describing spectroscopic emissions from this system. Now compute the frequency, wavelength and momentum of light emitted as the electron jumps from the n=5 to n=4 level. Do this by using the electron mass as well as the reduced mass. Why should the reduced mass give better results? Compute the percentage difference between the two. Using the Heisenberg Uncertainty relationship (ΔxΔp≥ℏ/2), estimate the radius of He+ for the n=5 level. You may assume the uncertainty in energy to be the same order as the energy of this level.arrow_forwardLearning Goal: To understand de Broglie waves and the calculation of wave properties. In 1924, Louis de Broglie postulated that particles such as electrons and protons might exhibit wavelike properties. His thinking was guided by the notion that light has both wave and particle characteristics, so he postulated that particles such as electrons and protons would obey the same wavelength-momentum relation as that obeyed by light: \ =h/p, where X is the wavelength, p the momentum, and h Planck's constant. X = 1.06×10-34 Submit Correct m Previous Answers -14 As a comparison, an atomic nucleus has a diameter of around 10 m. Clearly, the wavelength of a moving baseball is too small for you to hope to see diffraction or interference effects during a baseball game. Part C Consider a beam of electrons in a vacuum, passing through a very narrow slit of width 2.00 μm. The electrons then head toward an array of detectors a distance 0.9540 m away. These detectors indicate a diffraction pattern,…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSON
Introduction 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 Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College 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