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# HW1 - The integral you set up should be a function of n L x...

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EE2 Problem Set#1 Solutions Question #1: (5 points) Calculate the de Broglie wavelength of a particle with mass equal to 1.5 gm and moving with a velocity of 10 miles per hour. (Watch your units!) The de Broglie wavelength of a particle (mass m, velocity v) is given by h p h mv v = 4.47 meters/second m = 1.5*10 -3 kg h is the Planck’s constant ( = 6.626x10 -34 J-s) Therefore, 6.626 *10 34 1.5 *10 3 * 4.47 J * s kg * m / s 9.883*10 32 (This is incredibly small!!) Question #2: (5 points) What is the de Broglie wavelength of an electron that has a kinetic energy of 6 electronVolts (eV)? E = 6 eV = 6 x 1.602x10 -19 J = 9.612x10 -19 J We also know that E = p 2 /2m and the mass of an electron, m e = 9.1x10 -31 kg Therefore, p 2*9.11*10 31 *9.612*10 19 1.323*10 24 kg * m s As in problem 1, 6.626 *10 34 1.323*10 24 J * s kg * m s 5.009 *10 10 m 5 Å Question #3: (10 points) For a particle in a box that has width L and infinitely tall walls, what is the probability of finding a particle in L/4 < x < 3L/4.

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Unformatted text preview: The integral you set up should be a function of n , , L , x . We know the wave function for a particle in an infinite box is 2 L sin n x L and that the probability of finding a particle is 2 x 1 x 2 2 L sin n x L dx L 4 3 L 4 2 Question #4 (10 points) What is the change in energy (in electronVolts) when an electron moves from the n=2 level to the n=1 level of a Hydrogen atom? h 6.626 *10 34 J * s 1 eV 1 electronVolt 1 Volt * charge of one electron 1.6 *10 19 J Ú 8.85 *10 12 F m F Farad Coulomb Volt e 1.6 *10 19 C C Coulomb Volt Joule Coulomb E 1 2 m e 2 4 Ú h n 2 E ( n 2) E ( n 1) 10.19 eV...
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HW1 - The integral you set up should be a function of n L x...

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