A hydrogen atom is composed of one proton
at the nucleus and one electron that moves around the nucleus.
The electron does not move in a well-defined orbit but occupies a
sphere shape "cloud" that surrounds the nucleus. At the
lowest energy sate, the "cloud" can be assumed as a sphere
centered at the nucleus. The way to describe the motion of the electron
is to find the probability that the electron will be found within a certain area.
What is known:
The probability density function for the electron radial location is:
p(r) = 4/a3r2e-2x/a
where a is a constant. Its integral gives the probability that the
electron will be found within a certain area:
where r is the radius of the sphere centered at the nucleus where the
electron will be found and a is a constant.