Two Dimensional Well Exercise #7

Please answer the  following 2 questions regarding the Physlet:

Start of definite integral = End of definite integral = Graph: rmax=


The probability density, P(r) = y*y r2,  for an electron in an idealized Hydrogen atom (Coulomb potential) for several states is shown as plotted versus distance given in Bohr radii.  You can choose the limits of integrating by changing the values of "Start" and "End." Then select a wave function. 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.


  1. 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.
  2. For the three n = 3 states, find the radii at which the electron has a 50% probability of being inside and 50% outside.


Script by Mario Belloni.
Questions by Mario Belloni.
Java applets by Wolfgang Christian.