Answer
P(r) has its maximum value at the Bohr radius, a.
Work Step by Step
At the r where P(r) has its maximum value, $\frac{d}{dr}r^2|\Psi|^2=0$.
Using a result from Example 41.4, $r^2|\Psi|^2=Cr^2e^{-2r/a}$
Find the derivative.
$\frac{d}{dr}r^2|\Psi|^2= Ce^{-2r/a}(2r-\frac{2r^2}{a})$
This derivative is zero for r=a.
P(r) has its maximum value at the distance of the electron from the nucleus in the Bohr model.
This agrees with Figure 41.8 in the textbook.
