Two Dimensional Well Exercise #6

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.

Questions

  1. What is the probability that the electron in the n = 1, l = 0 (1s) state is at a distance greater than 1ao?
  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.

Credits

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