Physics for Scientists and Engineers with Modern Physics
Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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Chapter 38, Problem 22P
To determine

The proof that for a particle in a perfectly rigid box, the wavelength of the wave function for any state is the de Broglie wavelength.

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(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.
(c) Light of wavelength 450 nm is emitted by an electron in an atom behaving as a lightly damped simple harmonic oscillator with a Q value of 2×107. Find the natural frequency of the system in radians per second.
(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?

Chapter 38 Solutions

Physics for Scientists and Engineers with Modern Physics

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