Modified Mastering Physics With Pearson Etext -- Standalone Access Card -- For Physics For Scientists & Engineers With Modern Physics (5th Edition)
5th Edition
ISBN: 9780134402628
Author: Douglas C. Giancoli
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 38, Problem 21P
To determine
The proof that uncertainty principle holds for a “wave packet” formed by two similar waves; width of each wave packet is
Expert Solution & Answer
![Check Mark](/static/check-mark.png)
Want to see the full answer?
Check out a sample textbook solution![Blurred answer](/static/blurred-answer.jpg)
Students have asked these similar questions
(b) (deBroglie wave length) Determine the deBroglie wavelength (formula: p=h/2) of a
grain of dust with diameter 1um, density 1kg m-3 and speed 1cm s. Compare your
result with the diameter of the dust grain and the diameter of an atom. Comment?
(10) i) Use the quantum mechanical kinetic energy operator T, =
to find the kinetic energy of the first
2m dx?
excited state of the Particle in a Box (with n = 2). ii) Then, use the relationship of kinetic energy and momentum (KE
= p?/2m) to find an equation for the de Broglie wavelength of the particle in a one-dimensional box as a function only
of the box length L and quantum number n. iii) Sketch the wavefunction in the box to verify that the expression you
obtained in part ii) is correct.
(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 eVnm
Chapter 38 Solutions
Modified Mastering Physics With Pearson Etext -- Standalone Access Card -- For Physics For Scientists & Engineers With Modern Physics (5th Edition)
Knowledge Booster
Similar questions
- (a) Show that the spread of velocities caused by the uncertainty principle does not have measurable consequences for macroscopic objects (objects that are large compared with atoms) by considering a 100-g racquetball confined to a room 15 m on a side. Assume the ball is moving at 2.0 m/s along the x axis.arrow_forward(i) Compare stimulated and spontaneous emission. What is the significance of Einstein's coefficients? (ii) Calculate the frequency difference between resonant longitudinal 20th mode and 21th mode, if the cavity length is 20 cm.arrow_forward(b) Sketch and write the mathematical expression of the wavefunction of an electron occupying the level n 6 in a 1ID infinite quantum well of width 3.5x10" m. (c) A radio station broadcasts on a frequency of 200 kHz by using a 200 kW transmitter. () Estimate the number of photons striking a 1 square metre acrial each second at a distance of 1000 km. (ii) What is the energy () and momentum (kg m/s) of the photons? (ii) What is the number of photons emitted in 2 second by the transmitter?arrow_forward
- (i) Show that the classical Rayleigh-Jeans formula is a special case of Planck's radiation formula. (ii) Given a wave function of a particle as = Ae-ip/hy, confined such that 0arrow_forward(b) An electron confined in a one dimensional box emits a 200 nm photon in a quantum jump from n = 2 to n = 1. What is the length of the box? The mass of an electron is 9.11 x 1031 kg. (c) A proton confined in a one dimensional box emits a 2.0 MeV gamma-ray photon in a quantum jump from n = 2 to n = 1. What is the length of the box? The mass of a proton is 1.67 x 1027 kg.arrow_forwardAn electron and a proton, each initially at rest, are accelerated across the same voltage. Assuming that the uncertaintyin their position is given by their de Broglie wavelength,find the ratio of the uncertainty in their momentum.arrow_forward(c) Below is the expression of quantized subband energy in a quantum well photodetector where the m* and Wz are the carrier effective mass and well width, respectively, and the rest are constants. Derive the wavelength detected based on intersubband transition. En = ħ2 nn *W. 2m Zarrow_forwardThis question is for modern physics and wave and particle: (a) To how small a region must an electron be confined for borderline relativistic speeds – say, 0.05c – to become reasonably likely? (Ans: 3.9×10^−12m ) (b) On the basis of this, would you expect relativistic effects to be prominent for hydrogen’s electron, which has an orbit radius near 10-10? For a lead atom “inner-shell” electron of orbit radius 10-12m?arrow_forwardUse the uncertainty principle to show that if an electron were confined inside an atomic nucleus of diameter 2 x 10-15 m, it would have to be moving relativistically, whereas a proton confined to the same nucleus can be moving nonrelativistically.arrow_forward(i) Is an electron a particle? Is it a wave? Explain your answer citing relevant experimental evidence. Calculate the De-Broglie wavelength of an electron having a kinetic energy of 1000eV. Compare the result with wavelength of X-rays having the same energy.arrow_forwardConsider an electron with a (non-relativistic) kinetic energy of 1 eV. (i) What is the electron speed in m/s? What is the de Broglie wavelength of the electron? (ii) Consider a beam of 1 eV electrons incident on a pair of very thin slits, separated by a distance d, with an interference pattern seen on a screen 2 m beyond the slits. Find the value of d such that the position of the first off-center bright fringe of the pattern is located 0.5mm from the center of the pattern.arrow_forward7) A particular laser oscillating at the resonant wavelength of 1 um has a M value of 1010. The photon number in the cavity at the threshold pumping rate is (Write the Answer as an integral number without using exponents)arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_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
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305952300/9781305952300_smallCoverImage.gif)
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9780133969290/9780133969290_smallCoverImage.gif)
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
![Text book image](https://www.bartleby.com/isbn_cover_images/9781107189638/9781107189638_smallCoverImage.jpg)
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
![Text book image](https://www.bartleby.com/isbn_cover_images/9781337553278/9781337553278_smallCoverImage.gif)
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9780321820464/9780321820464_smallCoverImage.gif)
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134609034/9780134609034_smallCoverImage.gif)
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON