HW5S10Modern Physics

Modern Physics

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HW 5 S10 Modern Physics due at lecture F 16 April This is not group work! Problem 1: Spin Angular Momentum Compute the ratio S/L of the magnitudes of the spin angular momentum for a) An s-electron b) A p-electron c) A d-electron d) A f-electron Note that for all but the s-electron the size of the spin angular momentum is of the same order of magnitude as the orbital angular momentum. Problem 2: Stern-Gerlach Experiment Sketch the Stern-Gerlach experiment and explain its physical principles.
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Problem 3: Hydrogen atom The radial probability density for an electron is r 2 R 2 (r). That means that the probability of finding an electron at a certain radius r within a radial thickness dr is dr* r 2 R 2 (r) for an infinitely thin shell and approximately r* r avg 2 R 2 (r avg ) for a shell of finite thickness r. The quantity r avg is some average radius within the shell. (a) Estimate the probability that an electron in the n=1, l=0 state will be found in the region from r=0 to r= 10 -15 [m]. Use approximations in the probability function where necessary. Explain why the
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Unformatted text preview: approximation is valid. (b) Repeat the calculation for n=2, l=1. (c) Compare the two results, explain their difference, and explain the relevance of 10-15 [m] distance from the center of the atom. (d) Consider the state n=2, l=0 in hydrogen. What are the values of r for which the probability density is zero? Sketch the probability density as a function of r for this state. Problem 4: Quantization of Angular Momentum (a) The allowed magnitudes of angular momentum are . Use the binomial expansion to prove that when l is large, . What does this result say about the agreement between the Bohr model and modern quantum mechanics? (b) For a given magnitude of , what is the largest allowed value for L z ? Prove that this largest value is less than or equal to L. (c) Draw a vector model diagram for the cases l=2, l=3. Find the minimum possible angle between L and the z axis. Hint: Refer to figure in last W lectures hand out....
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HW5S10Modern Physics - approximation is valid. (b) Repeat...

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