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EE 2 HW 1 09Spring-PS1-Solns

# EE 2 HW 1 09Spring-PS1-Solns - EE2 Problem Set#1 Solutions...

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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 λ = 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 24 J * s kg * m = 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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EE 2 HW 1 09Spring-PS1-Solns - EE2 Problem Set#1 Solutions...

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