In this problem you will show that the charge density of the filled n = 2, l = 1 subshell is spherically symmetrical and that therefore L = 0. The angular distribution of the electron charge is simply the sum of the squares of the magnitude of the angular part of the wave functions for l = 1 and ml = ˆ’1, 0, and 1.

a. Given that the angular part of these wave functions is

write an expression for

b. Show that

c. Why does this result show that the charge density for the filled n = 2, l = 1 subshell is spherically symmetrical?

3 42 Cos e 3 (e. 6) 1/2 x(e. ) 3 sin ee /2 sin ee 3