Question

df- Adobe Reader 43.12 Consider the tollowing problem (Stewart 2006). The hydrogen atom con- sists of one proton in the nucleus and one electron, which moves about the nucleus. The electron does not move in a well-defined orbit, but there is a probability for finding the electron at a certain distance from the nucleus. The PDF is given by p(r)-47 exp(-2 r/ao) /a03 for r2 0, where a,- 5.59 x 101 m is the Bohr radius. The integral over this PDF from zero to r gives the probability that the electron will be found within a sphere of radius r meters centered at the nucleus. a) Calculate the mean distance R of the electron from the nucleus. b) Calculate the variance of the PDF c) Show that the PDF is a gamma PDF. Hint: use n1) nt for integer values of n. d) For what value of r does p) have its maximum value? e) Find the probability that the electron will be within the sphere of radius 3 ao centered at the nucleus. Hint: the following integrals will be helpful (a is any constant). 一丁(a-x"-2ax + 2 CT Activate (7 46 0 8

Answer 1

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