Homework 9 - PHYSICS 309L, Spring 2010 HOMEWORK 9, due...

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Unformatted text preview: PHYSICS 309L, Spring 2010 HOMEWORK 9, due Monday 04/26/10 1. A particle is confined in a cubic box, each side measures 1Angstrom. The mass of the particle is 10−30 kg . The potential energy inside the box is zero, outside the box it is infinite. Use the Heisenberg uncertainty principle to find the lowest possible momentum for the particle and calculate the lowest possible energy for this particle in eV. 2. Consider an harmonic oscillator with spring constant k and mass m. - Find the classical frequency of this oscillator as a function of the spring constant and m. In quantum mechanics, the spectrum of possible energies for this oscillator is given by: En = hf (N +1/2) where n is a natural number: n = 0, 1, 2, 3, ..., h is Planck’s constant and f is the frequency. - Find the ground state energy as a function of the spring constant and the mass. - What is the difference of energy between the second excited state and the ground state? - Assume now that the oscillator carries a unit of charge, what is the wavelength of the photon emitted as a function of k and m when the oscillator goes from the first excited state down to the ground state? 2 - What is the wavelength of the emitted photon of the previous question if k = 10eV /˚ , A where ˚ denotes Angstrom and eV: electron volt. Is the emitted photon in the visible A spectrum of a human eye? ...
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This note was uploaded on 10/20/2011 for the course PHY 309L taught by Professor Sai during the Spring '08 term at University of Texas at Austin.

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