Modern Physics For Scientists And Engineers
2nd Edition
ISBN: 9781938787751
Author: Taylor, John R. (john Robert), Zafiratos, Chris D., Dubson, Michael Andrew
Publisher: University Science Books,
expand_more
expand_more
format_list_bulleted
Question
Chapter 4, Problem 4.28P
To determine
(a)
The momentum
To determine
(b)
The proof that answer agree with result from Compton's formula for
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
An electron with kinetic energy E = 3.10 eV is incident on a barrier of width L = 0.230 nm and height U = 10.0 eV
(a)
What is the probability that the electron tunnels through the barrier? (Use 9.11 10-31 kg for the mass of an electron, 1.055 ✕ 10−34 J · s for ℏ, and note that there are 1.60 ✕ 10−19 J per eV.)
b)
What is the probability that the electron is reflected?
What If? For what value of U (in eV) would the probability of transmission be exactly 25.0% and 50.0%?
c) 25.0%
d) 50.0%
Consider an electron confined to a box of length L = 436 pm.
(a) A transition between energy levels can be induced by absorption of light whose photon
energy matches the energy difference between the levels. Find the energy difference
between the levels corresponding to n = 4 and n = 5 of this same box, and compute the
wavelength of light (in m) that would cause a transition between them. What portion of
the electromagnetic spectrum is this light?
(b) For another box, suppose that this same transition (n = 4 → 5) was observed at a
wavelength of 232 nm. How long is this box in pm?
A particle of mass 1.60 x 10-28 kg is confined to a one-dimensional box of length 1.90 x 10-10 m. For n = 1, answer the following.
(a) What is the wavelength (in m) of the wave function for the particle?
m
(b) What is its ground-state energy (in eV)?
eV
(c) What If? Suppose there is a second box. What would be the length L (in m) for this box if the energy for a particle in the n = 5 state of this box
is the same as the ground-state energy found for the first box in part (b)?
m
(d) What would be the wavelength (in m) of the wave function for the particle in that case?
m
Chapter 4 Solutions
Modern Physics For Scientists And Engineers
Ch. 4 - Prob. 4.1PCh. 4 - Prob. 4.2PCh. 4 - Prob. 4.3PCh. 4 - Prob. 4.4PCh. 4 - Prob. 4.5PCh. 4 - Prob. 4.6PCh. 4 - Prob. 4.7PCh. 4 - Prob. 4.8PCh. 4 - Prob. 4.9PCh. 4 - Prob. 4.10P
Ch. 4 - Prob. 4.11PCh. 4 - Prob. 4.12PCh. 4 - Prob. 4.13PCh. 4 - Prob. 4.14PCh. 4 - Prob. 4.15PCh. 4 - Prob. 4.16PCh. 4 - Prob. 4.17PCh. 4 - Prob. 4.18PCh. 4 - Prob. 4.19PCh. 4 - Prob. 4.20PCh. 4 - Prob. 4.21PCh. 4 - Prob. 4.22PCh. 4 - Prob. 4.23PCh. 4 - Prob. 4.24PCh. 4 - Prob. 4.25PCh. 4 - Prob. 4.26PCh. 4 - Prob. 4.27PCh. 4 - Prob. 4.28PCh. 4 - Prob. 4.29PCh. 4 - Prob. 4.30PCh. 4 - Prob. 4.31PCh. 4 - Prob. 4.32PCh. 4 - Prob. 4.33P
Knowledge Booster
Similar questions
- 6.5 C Consider the impact of early electron diffraction experiments on scientists’ understanding ofthe behavior of matter. Which of the following imaginary macroscopic experiments most closely corresponds to the remarkable outcome ofelectron diffraction?(a) Combining one marble with another by one method yields two marbles; but combining the two marbles by another method yields four marbles.(b) Combining one marble with another by one method yields two marbles; but combining the two marbles by another method yields zero marbles.(c) Combining one marble with another by any method yields two marbles.arrow_forwardWhat is the maximum possible energy for a Compton-backscattered x ray (θ = 180°)? Express your answer in terms of , the wavelength of the incoming photon. (b) Evaluate numerically when the incoming photon’s energy is 100 keVarrow_forward(a) Calculate the minimum uncertainty in momentum (expressed in MeV/?) for a proton confined to a nucleus of diameter 5.0 fm. (1 fm = 1 * 10-15 m). (b) A proton (rest mass 938.3 MeV/?2) in a nucleus of radius 6.0 fm has a kinetic energy of 5.6 MeV. If the proton were represented by a de Broglie wave, how many wavelengths could fit across the diameter of that nucleus? (1 fm = 1 * 10-15 m). (c) Electrons (rest mass 0.51 MeV/?2) moving with a speed of 1.60 × 105 m/s are described by a wave packet of width 2.65 nm. What range of values will most likely result from a measurement of the speed of the electrons? Please use:ℎ? 1240 eVnmℏ? 197 eVnmarrow_forward
- An electron with kinetic energy E = 5.50 eV is incident on a barrier of width L = 0.190 nm and height U = 10.0 eV. Energy 0 (a) What is the probability that the electron tunnels through the barrier? (Use 9.11 × 10-31 kg for the mass of an electron, 1.055 × 10¯³4 J · s for h, and note that there are 1.60 × 10¯ % (b) What is the probability that the electron is reflected? % What If? For what value of U (in eV) would the probability of transmission be exactly 25.0% and 50.0%? (c) 25.0% (d) 50.0% eV eV -19 J per eV.)arrow_forward= = An electron having total energy E 4.60 eV approaches a rectangular energy barrier with U■5.10 eV and L-950 pm as shown in the figure below. Classically, the electron cannot pass through the barrier because E < U. Quantum-mechanically, however, the probability of tunneling is not zero. Energy E U 0 i (a) Calculate this probability, which is the transmission coefficient. (Use 9.11 x 10-31 kg for the mass of an electron, 1.055 x 10-34] s for h, and note that there are 1.60 x 10-19 J per eV.) (b) To what value would the width L of the potential barrier have to be increased for the chance of an incident 4.60-eV electron tunneling through the barrier to be one in one million? nmarrow_forwardConsider two experiments involving a metal sphere with a radius of 2.00 μm that is suspended in a vacuum. In one experiment, a pulse of N photons reflects from the surface of the sphere, causing the sphere to acquire momentum. In a second experiment, an identical pulse of photons is completely absorbed by the sphere, so that the sphere acquires momentum. Identify each type of collision as either elastic or inelastic, and, assuming that the change in the photon wavelength can be ignored, use linear momentum conservation to derive the expression for the momentum of the sphere in each experiment.arrow_forward
- Find the Fourier transform of rect(t/4). 2. (a) sinc(w) (b) sinc(w) (c) sinc(2w) (d) 2 sinc(2w) Type here to searcharrow_forwardGas molecules in our atmosphere have sizes (~ 10 À) much smaller than the wave- length of optical photons. As a result, bound electrons within the molecules preferentially scatter shorter wavelength photons (Rayleigh scattering). The photon cross-section o for Rayleigh scattering goes as A-4, where A is the photon wavelength. Obtain an expression for the typical travel time of a red photon (A = 8000 Å) across a layer of atmosphere with thick- ness d, knowing that a blue photon (A = 4000 Á) has a mean-free-path length lImfp = d/3 in the same atmosphere. Express your answer using d and c, where c is the speed of light.arrow_forwardProblem 1: (a) A non-relativistic, free particle of mass m is bouncing back and forth between two perfectly reflecting walls separated by a distance L. Imagine that the two oppositely directed matter waves associated with this particle interfere to create a standing wave with a node at each of the walls. Find the kinetic energies of the ground state (first harmonic, n = 1) and first excited state (second harmonic, n = 2). Find the formula for the kinetic energy of the n-th harmonic. (b) If an electron and a proton have the same non-relativistic kinetic energy, which particle has the larger de Broglie wavelength? (c) Find the de Broglie wavelength of an electron that is accelerated from rest through a small potential difference V. (d) If a free electron has a de Broglie wavelength equal to the diameter of Bohr's model of the hydrogen atom (twice the Bohr radius), how does its kinetic energy compare to the ground-state energy of an electron bound to a Bohr model hydrogen atom?arrow_forward
- Consider the Compton scattering of a photon of wavelength Ao by a free electron moving with a momentum of magnitude P in the same direction as that of the incident photon. (a) Show that in this case the Compton equation (1.42) becomes (ро + P) с sin? AX = 240 E – Pc 2 h/Ao is the magnitude of the incident photon momentum, 0 is the photon scattering angle where po 1/2 and E = (m²c* + P²c²)*/² is the initial electron energy.arrow_forwardV,E -V. Consider the potential well of depth V, and width w, as shown in the figure above. An electron with energy Ɛ > 0 is incident from the left. (a) Determine the condition involving the incident energy (E) and the depth (V.) and width (w) of the well for resonant transmission in which there is no reflected wave associated with the electron. (b) If 4(x) = Aejkx is the incident electron wave for x w) the well, under resonant conditions?arrow_forwardA 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)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