Question

34. An electron in the 3d state of the hydrogen atom has a radial part of the wave function of the form A r2 exp(-r/3ao). What is the most likely radius at which the electron would be found? a. 2ao b. 3ao c. 4ao d. 5ao e. 9ao

Answer 1

Answer: Option (e) is the correct answer.

Explanation:

Formula to calculate radius is as follows.

          p(r) = $Ar(r^{2}e^{\frac{-r}{3a_{o}}}$

                = $Ar^{3}e^{\frac{-r}{3a_{o}}}$

     $\frac{dp(r)}{dr}$ = 0

            $Ar^{3}e^{\frac{-r}{3a_{o}}}(\frac{-1}{3a_{o}}$ + $Ae^{\frac{-r}{3a_{o}}}(3r^{2})$ = 0

                     $\frac{Ar^{3}}{3a_{o}}e^{\frac{-r}{3a_{o}}}$

                      = $3Ar^{2}e^{\frac{-r}{3a_{o}}}$

                       r = $9a_{o}$

Thus, we can conclude that most likely radius at which the electron would be found is $9a_{o}$.