The radial wave function for the 2p shell of hydrogen is: R_{2 p}(r)=\frac{r}{\sqrt{24 a^{5}}} \exp (-r / 2 a) where a = (me/m)ao, m is the reduced mass, m̟ is

the electron mass, and a, is the Bohr radius. Find the value of r for which the radial probability density is a maximum. ii. Verify that the wave function is correctly normalized. The following definite integral should be helpful: \int_{0}^{\infty} x^{n} e^{-\alpha x} \mathrm{~d} x=\frac{n !}{\alpha^{n+1}} \quad(n \geq 0 \text { and } \alpha>0)