4. A photon passes through a horizontal slit of width 5 x 10-6 m. What uncertainty in the verticalposition will this photon have as it emerges from the slit? What is the minimum uncertainty inthe vertical momentum?5. The speed of an electron is measured to within an uncertainty of 3 x 105 m/s. What is the sizeof the smallest region of space in which the electron can be confined?6. Estimate the typical range of outcomes of measurements of the rest energy of a hypotheticalparticle whose rest energy is 1 GeV and has a lifetime of 10-15 s.7. For a relativistic particle (of mass m and speed v), show that the following de Broglie relationshipsfor frequency and wavelength A hold:V =Xme²/h√1-v²/c²'mv/h√1-v²/c²Then show that the phase velocity and the group velocity of the de Broglie waves for such aparticle can be given by:Vg = v.

Answered: Image /qna-images/answer/99e4c95a-d736-44a2-bc6b-a9c43adb6611.jpg

4. A photon passes through a horizontal slit of width 5 x 10-6 m. What uncertainty in the vertical position will this photon have as it emerges from the slit? What is the minimum uncertainty in the vertical momentum?

4. A photon passes through a horizontal slit of width 5 x 10-6 m. What uncertainty in the vertical position will this photon have as it emerges from the slit? What is the minimum uncertainty in the vertical momentum?

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter28: Quantum Physics

Section: Chapter Questions

Problem 20CQ

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Concept explainers

de Broglie Equation

The sketch of matter waves is drawn below:

Question

4. A photon passes through a horizontal slit of width 5 x 10-6 m. What uncertainty in the vertical
position will this photon have as it emerges from the slit? What is the minimum uncertainty in
the vertical momentum?
5. The speed of an electron is measured to within an uncertainty of 3 x 105 m/s. What is the size
of the smallest region of space in which the electron can be confined?
6. Estimate the typical range of outcomes of measurements of the rest energy of a hypothetical
particle whose rest energy is 1 GeV and has a lifetime of 10-15 s.
7. For a relativistic particle (of mass m and speed v), show that the following de Broglie relationships
for frequency and wavelength A hold:
V =
X
me²/h
√1-v²/c²'
mv/h
√1-v²/c²
Then show that the phase velocity and the group velocity of the de Broglie waves for such a
particle can be given by:
Vg = v.

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