Part d Problem 1:(a) A non-relativistic, free particle of mass m is bouncing back and forth between two perfectly reflectingwalls separated by a distance L. Imagine that the two oppositely directed matter waves associated with thisparticle interfere to create a standing wave with a node at each of the walls. Find the kinetic energies of theground state (first harmonic, n = 1) and first excited state (second harmonic, n = 2). Find the formula forthe 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 largerde Broglie wavelength?(c) Find the de Broglie wavelength of an electron that is accelerated from rest through a small potentialdifference V.(d) If a free electron has a de Broglie wavelength equal to the diameter of Bohr's model of the hydrogenatom (twice the Bohr radius), how does its kinetic energy compare to the ground-state energy of an electronbound to a Bohr model hydrogen atom?

Answered: Image /qna-images/answer/61f62c1a-1815-45e7-a804-29bd591ae7c8.jpg

(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?

(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?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Free Body Diagram

The system of forces acting on a body tends to either rotate it or make the body undergo motion. In general, when an external agent exerts a force on a body, the body undergoes translational motion and rotational motion. The body has six degrees of freedom under the influence of that force. Here, three degrees of freedom are from the translational motion while the other three are from the rotation motion. However, sometimes the bodies are not allowed to undergo any motion and are fixed, under such conditions the body is said to be constrained.

Question

Part d

Problem 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?

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