If we think of an electron as a particle, the function P(r)=1 (2r2 + 2r + 1)e 2r is the
Chapter 8, Problem 17(choose chapter or problem)
If we think of an electron as a particle, the function P(r)=1 (2r2 + 2r + 1)e 2r is the cumulative distribution function of the distance, r, of the electron in a hydrogen atom from the center of the atom. The distance is measured in Bohr radii. (1 Bohr radius = 5.29 1011 m. Niels Bohr (18851962) was a Danish physicist.) For example, P(1) = 1 5e2 0.32 means that the electron is within 1 Bohr radius from the center of the atom 32% of the time. (a) Find a formula for the density function of this distribution. Sketch the density function and the cumulative distribution function. (b) Find the median distance and the mean distance. Near what value of r is an electron most likely to be found? (c) The Bohr radius is sometimes called the radius of the hydrogen atom. Why?
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