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.

Step-by-step explanation:

Formula to calculate radius is as follows.

p(r) =
`Ar(r^(2)e^{(-r)/(3a_(o))}`

=
`Ar^(3)e^{(-r)/(3a_(o))}`

`(dp(r))/(dr)` = 0

`Ar^(3)e^{(-r)/(3a_(o))}((-1)/(3a_(o))` +
`Ae^{(-r)/(3a_(o))}(3r^(2))` = 0

`(Ar^(3))/(3a_(o))e^{(-r)/(3a_(o))}`

=
`3Ar^(2)e^{(-r)/(3a_(o))}`

r =
`9a_(o)`

Thus, we can conclude that most likely radius at which the electron would be found is
`9a_(o)`.