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Homework 9

# Homework 9 - PHYSICS 309L Spring 2010 HOMEWORK 9 due Monday...

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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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