## Problem 13.6: The probability density for an electron in an idealized Hydrogen atom

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The probability density, *P*(*r*) = *R*^{2}(*r*)*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 change the start and end of the integral as well as the range plotted in the graph by changing values and clicking the "evaluate" button.

- For the three
*n*= 3 states, find the radii at which the electron has a 50% probability of being inside and 50% outside. - 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. - The
*n*= 3,*l*= 1 (3p) state has two regions in which the electron may be located. Find the probabilities of finding the electron in each of the two regions.