Question

Problem 4 Consider the hydrogenic wavefunctions Un,1,mi = Rn,l(r)Yı,mı (0,0) for an elec- tron in a hydrogen atom (Z = 1). The electron is in the 2s state. a) Determine the location of the radial node in terms of ao. b) Calculate the most probable radius of an electron in a 2s state, and com- pare this radius with the most probable radius of the ls state (ao). c) Using the formula provided in class, determine the mean radius for the 2s electron. d) Compare the mean radius and the location of the node. Is the electron most likely to be found at r larger or smaller than the location of the node?

Answer 1

S n =2, P=0 Rulwali za Probability cy Anidiny & bw resedy - Prodo = 12.00? 4xr²dr Po dr = 1 1 1 1 - 2 ) 2 a wrot dr PM (1 ) el PO) (*+ y ) Na for most probable vale d o to hotelov + 2 ) Ya+60+ lar. 192Ymp formy Imp Imp? - sarme +162² mp + 80² - 0 (ymp+uQ) / Ymp – lo ax +442) = 0 Ymp =- a this in alto nos a enim 100+ [100021692 so mi - 1048 + vo-0 -2

por 100+ 9.1654 - 9.58a 10a-gorosa = 0.4175a (mp). = 100 9.1659 e ymp) Bohr radics, so Answer should be limp). STR )? o x odebralie/ dy [I (1 + -el.de De di tal vs You - . 49² Jaya omi] by POV ( 304 + soap on w - ? [ 6 +30 24] on