Reference no: EM131607451

Question: 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 × 10^-11 m. Niels Bohr (1885-1962) was a Danish physicist.) For example, P(1) = 1 - 5e^-2 ≈ 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?