## Two Dimensional Well Exercise #7

#### Please answer the following 2 questions
regarding the Physlet:

#### Description

The probability density, P(r) = y*y
r^{2}, 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, *a*_{0}
= 0.0529 nm.

#### Questions

- Consider the
*n* = 2, *l* = 0 (2s) and *l* = 1
(2p)states. Compare the probabilities for the electron to be within 2*a*_{o}
in the two states and the probabilities that it is outside 5*a*_{o.}
Interpret this result in light of the angular momentum of the two states.
- For the three
*n* = 3 states, find the radii at which the electron
has a 50% probability of being inside and 50% outside.

#### Credits

Script by Mario Belloni.

Questions by Mario Belloni.

Java applets by Wolfgang Christian.