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E45_PS_2-2011

# E45_PS_2-2011 - E45 Problem Set No 2 Due 5:00pm Friday Note...

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E45 Problem Set No. 2 Due: 5:00pm, Friday 9/16/11 Note: h= Planck’s Constant = 6.625x10 -34 Joule . second ε o = 8.8542 x 10 -12 coulomb/volt . meter m=mass of electron = 9.1085X10 -28 g e= charge of electron = 1.6021X10 -19 coulomb 1. Outline two experiments, one showing the electron to be a particle, the other showing it to be a wave. 2. A dust particle of mass 10 -6 g travels in outer space at a velocity of 25,000 mph. Calculate its wavelength. 3. What is the momentum of photons of red light ( λ =6,500 Å)? 4. Show that the maximum value of the probability density function for the 1s orbital of the hydrogen atom is r max = 8 π ε o h 2 /4 π 2 me 2 . Calculate the value of r max and compare it to the value of the Bohr radius of the hydrogen atom, 0.5292 Å. 5. Explain why it is necessary to use the intensity ( ψ 2 ) of the probability amplitude ( ψ ) in order to provide a physical interpretation of the mathematical expression ψ = A exp[2 i(x/ π λ + ν t). 6. Show that the maximum value of the probability density function for the 1s orbital of the hydrogen atom occurs at r max

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E45_PS_2-2011 - E45 Problem Set No 2 Due 5:00pm Friday Note...

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