(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.

(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.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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