quiz01 - wavelength in the order of its size of about 1cm...

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Quiz # 1, Physics 316, Modern Physics I Date: Wednesday, 02/25/05 - 9:05, 132 Rockefeller Hall Exercise 1: Black-body radiation has a spectral power distribution which has its maximum at about ν = 350THz for a temperature of T 1 = 6000K. Where will it have its maximum for T 2 = 2000K? If a black body emits P = 1kW at T 1 = 6000K, what power does it emit at T 2 = 2000K? Exercise 2: If electrons with kinetic energy K e hit a medium and produce Bremsstrahlung, its maximum frequency is ν max = K e /h if the Work-function is neglected. How does this formula change if the Work-function W is not neglected? Exercise 3: The Balmer line of Hydrogen with lowest frequency is at ν B = 457THz, in the visible region. The Frst Lyman line is in the ultraviolet. What is its frequency ? Exercise 4: How slow would a marble with a mass of 1g have to be in order to have a de Broglie
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Unformatted text preview: wavelength in the order of its size of about 1cm? Exercise 5: Given an inFnite potential well between x = 0 and x = L and a wave function that has the form Ψ( x, 0) = 4 q 1 5 L sin 3 ( x π L ) at time t = 0 inside the well, what is the time dependent solution Ψ( x,t ) of the Schr¨ odinger equation? The following may be helpful: sin( φ ) = 1 2 i ( e iφ-e-iφ ) . (1) Exercise 6: In the following Fgures the Frst three stationary states are drawn for a potential of the form V ∝ 1 /x for x > 0 and V = ∞ for x < 0. The potential and the energy levels are also drawn. Which qualitative properties of one dimensional wave functions can you observe? Φ( x ) Φ( x ) Φ( x ) V ( x ) V ( x ) V ( x ) E E E x x x...
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