ECE331 Homework #3 (Due Friday, April 25, 2008) 1. (a) The position of an electron is determined to within 1 A o . What is the minimum uncertainty in its momentum? (b) An electron’s energy is measured with an uncertainty of 1 eV. What is the minimum uncertainty in the time over which the measurement was made? 2. What is the de Broglie wavelength (in A o ) of an electron at 100 eV? What is the wavelength for electrons at 12 KeV, which is typical of electron microscopes? Comparing this to visible light, comment on the advantages of electron microscopes. 3. We define a potential well having energies V as a function of position x, as follows: V = ∞ for x = -0.5nm to 0; V = 0 eV for x = 0 to 5 nm; V = 10 eV for x = 5 to 6 nm, and V = 0 for x > 6 nm and x < -0.5 nm. We put an electron with energy 7 eV in the region x , between 0 and 5 nm. What is the probability of finding the electron at x < 0 nm? Is the probability of finding the electron at x > 6nm zero or nonzero? What is this probability for x > 6 nm if the electron was
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