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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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