If we think of an electron as a particle, the function is the cumulative distribution function of the distance, , of the electron in a hydrogen atom from the center of the atom. The distance is measured in Bohr radii. (1 Bohr radius meters. Niels Bohr (1885-1962) was a Danish physicist.)

For example, means that the electron is within Bohr radius from the center of the atom per cent of the time.

  1. Find a formula for the density function of this distribution. Sketch the density function and the cumulative distribution function.

  2. Find the median distance and the mean distance. Near what value of is an electron most likely to be found?
    Mean =
    Median =
    Most likely distance =

You should be able to explain why the Bohr radius is sometimes called the "radius of the hydrogen atom".

You can earn partial credit on this problem.