Answer: Option (e) is the correct answer.
Explanation:
Formula to calculate radius is as follows.
p(r) = [tex]Ar(r^{2}e^{\frac{-r}{3a_{o}}}[/tex]
= [tex]Ar^{3}e^{\frac{-r}{3a_{o}}}[/tex]
[tex]\frac{dp(r)}{dr}[/tex] = 0
[tex]Ar^{3}e^{\frac{-r}{3a_{o}}}(\frac{-1}{3a_{o}}[/tex] + [tex]Ae^{\frac{-r}{3a_{o}}}(3r^{2})[/tex] = 0
[tex]\frac{Ar^{3}}{3a_{o}}e^{\frac{-r}{3a_{o}}}[/tex]
= [tex]3Ar^{2}e^{\frac{-r}{3a_{o}}}[/tex]
r = [tex]9a_{o}[/tex]
Thus, we can conclude that most likely radius at which the electron would be found is [tex]9a_{o}[/tex].
