Hydrogen atom
The radial probability density for an electron is r2R2(r). That means that the probability of finding an electron at a certain radius r within a radial thickness dr is dr* r2R2(r) for an infinitely thin shell and approximately r* r2avg R2(ravg) for a shell of finite thickness r.
The quantity ravg is some average radius within the shell.
(a) Estimate the probability that an electron in the n=1,l=0 state will be found in the region from r=0m to r= 10-15m.
(b) Repeat the calculation for n=2, l=1.
(c) Compare the two results, explain their difference, and explain the relevance of 10-15m distance from the center of the atom.
(d) Consider the state n=2, l=0 in hydrogen. What are the values of r for which the probability density is zero?
Sketch the probability density as a function of r for this state.