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Q11S - 1 3 A compact way of writing the Bohr energy level...

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Quiz 11 Solutions Check the best answer. 1. The only experimental fact about the photoelectric effect that is consistent with classical theory is: If the incident light has frequency below a certain number, no electrons are released. [Should depend on intensity, not frequency.] The maximum kinetic energy of the released electrons rises linearly with the frequency of the incident light. [Same as above.] The maximum kinetic energy of the released electrons is independent of the intensity of the incident light. [Same as above.] The number of electrons released per second is proportional to the intensity of the incident light. [Number of photons per second is proportional to the intensity.] Check T or F depending on whether the statement is true or false. 2. If all the material in our solar system had been built up from light elements by fusion and neutron capture, we would find elements no more massive than iron. T F Physics 54 Summer 2011
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Unformatted text preview: 1 3. A compact way of writing the Bohr energy level formula for hydrogen is E n = − α 2 mc 2 2 n 2 , where = ke 2 / c ≈ 1/137 is a dimensionless number, and m is the electron mass. Use the classical relations for a circular orbit: K = − 1 2 U , and U = − ke 2 / r for the electron-proton system. a. Derive the formula v n = c 1 n for the electron’s speed in the n th orbit. b. Derive the formula r n = mc n 2 for the radius of the n th orbit. c. Show from these that the angular momentum is given by L = n . a. Since K + U = E and U = − 2 K we see that K = − E , so we set 1 2 mv n 2 = 2 mc 2 2 n 2 and Fnd the claimed result. b. Since K + U = E and K = − 1 2 U we see that E = 1 2 U . We set − 2 mc 2 2 n 2 = − 1 2 ke 2 / r n = − 1 2 c / r n , and Fnd the claimed result. c. Since L n = mv n r n , we Fnd the claimed result. Physics 54 Summer 2011 2...
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