hw1solution_1101

hw1solution_1101 - ECE G201 Homework 1 Solutions Problem 1...

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Homework 1 Solutions. Problem 1. This is easy and self-checking. Problem 2. Solution (from Prof. Hopwood) The He + is essentially identical to the H atom, except that the nucleus has a +2 charge. Therefore, the attract ion force between the remaining electron and the nucleus is F = -2q 2 /(4 πε o r 2 ) which is balanced by the force holding the electron in "orbit" F = mv 2 /r Applying the Bohr hypothesis that the angular momentum is quantized, p Θ = mvr = n X results in discrete energy levels E n = E vac – 2q 4 m/(4 πε o n X ) 2 = E vac – 2(1.609x10 -19 C) 4 (9.11x10 -31 kg)/[(4 π )(8.54x10 -12 F/m)(n)(1.06x10 -34 )] 2 (Joules) = E vac – 54.56/n 2 (eV) since 1 eV = 1.609x10 -19 Joules. The lowest six allowed energy levels for an electron in a He ion are: n=1 -54.56 eV n=2 -13.64 eV n=3 -6.063 eV n=4 -3.41 eV n=5 -2.182 eV n=6 -1.516 eV where each energy is relative to E vac The wavelength of light associated with the photon emitted as an electron transitions from a high energy level to a low energy level is related to the change in electron energy
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This note was uploaded on 03/22/2012 for the course ECE G201 taught by Professor Nm during the Spring '11 term at Northeastern.

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hw1solution_1101 - ECE G201 Homework 1 Solutions Problem 1...

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