Physical Chemistry Third Edition

748 17 The Electronic States of Atoms. I. The Hydrogen Atom

The 3dz^2 Orbital Region The 3pz Orbital Region The 3s Orbital Region

The 2pz Orbital Region The 2s Orbital Region

Figure 17.9 Some Orbital Regions of Hydrogen-Like Orbitals.Positive regions are in

black and negative regions are in gray.

Pictures of orbital regions are included in elementary chemistry and organic

chemistry textbooks, but sometimes the distinction between the orbital and the orbital

region is not emphasized. The orbital is a wave function, whereas the orbital region is

a three-dimensional region in space, inside which the magnitude of the orbital function

is larger than some specified small value.

PROBLEMS

Section 17.4: The Orbitals of the Hydrogen-Like
Atom

17.27a. Sketch the nodal surfaces for the first five energy
eigenfunctions for a particle in a three-dimensional
spherical box.Hint:The spherical harmonic functions

are the same as with the hydrogen atom, and the

pattern of nodes in the radial function is the same as

with the hydrogen atom, except that the nodal sphere at

infinity is replaced by a nodal sphere at the surface of

the box.