## Hydrogen Radial Probability Densities

 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 probability. If you click on P10 before clicking another button you will see all plots simultaneously. Use "Set r Scale" and "Set P(r) Scale" for the n = 2 and 3 states. 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 = 0.529 nm

Question 1:  Find the most probable radius of the electron in each of the six states.

Question 2:  For states with more than one value of l, in which state does the most probable radius equal the radius predicted by the Bohr model.

Question 3:  Explain qualitatively why the maximum value of the probability density is smaller for states with higher values of n.

This page Authored by Paul Zitzewitz, modified by Scott Schneider.