Question #bc2e5

Well... because they are spheres... which are infinitely symmetric in all three coordinate directions. And they are spheres because they have no angular momentum.

You can see that since for #s# orbitals, the angular momentum quantum number is simply #l = 0#.

And that ultimately comes from the fact that in no #s# orbital wave function is there an angular dependence.

A hydrogen atom wave function can be written as:

#psi_(nlm_l)(r,theta,phi) = R_(nl)(r)Y_(l)^(m_l)(theta,phi)#

where #n#, #l#, and #m_l# are the principal quantum number, angular momentum quantum number, and magnetic quantum number, respectively.

An example is the #2s# wave function:

#psi_(2s) = psi_(200)(r,theta,phi)#

#= 1/(4sqrt(2pi))(Z/a_0)^"3/2" (2 - (Zr)/a_0)e^(-Zr//2a_0)#

where #a_0 = "0.0529177 nm"# is 1 bohr radius, #r# is the radial distance away from the nucleus, and #Z = 1# is the atomic number of hydrogen atom.

You can see there is no #theta# or #phi# in the equation, so the #2s# orbital (as with any other #s# orbital) has no angular dependence.

Therefore, the wave function is only a function of the radial distance, and can only correspond to a spherical orbital.