Hydrogen Radial Probability Densities

and their integrals


rmax=  P(r)max= 

n = 1, l = 0    P(r) = r2 {2 e-r }2
n = 2, l = 0   P(r) = r2{ (1 - r/2) e-r/2 / sqrt(2) }2
n = 2, l = 1   P(r) = r2 { r e-r/2 / sqrt(24) }2
n = 3, l = 0   P(r) = r2{ 2/sqrt(27) (1 - 2r/3 + 2r2/27) e-r/3 }2
n = 3, l = 1   P(r) = r2 { 8/(27 sqrt(6)) r (1 - r/6) e-r/3 }2
n = 3, l = 2   P(r) = r2 { 4/(81 sqrt(30)) r2 e-r/3 }2		 Instructions: First click on Plot P10. Then plot any other wavefunction. If you click on P10 before clicking another button you will see all plots simultaneously. Use "Set r Scale" to see the entire plot of the n = 2 and 3 states. Use "Set P(r) Scale" to expand the graph as needed. Place cursor on graph and press left mouse button to read coordinates. Press right mouse button to copy graph to a new window.
Note:  All distances are in units of Bohr radii,
a0 = 0.0529 nm
Question 1: What is the probability that the electron in the n = 1, l = 0 (1s) state is at a distance greater than 1ao?

Question 2: The n = 3, l = 0 (3s) state has three regions in which the electron may be located.  Find the probabilities of finding the electron in each of the three regions.

Question 3: Consider the n = 2, l = 0 (2s) and l = 1 (2p)states.  Compare the probabilities for the electron to be within 2ao in the two states and the probabilities that it is outside 5ao. Interpret this result in light of the angular momentum of the two states.

Question 4:  For the three n = 3 states, find the radii at which the electron has a 50% probability of being inside and 50% outside.

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