Organic Chemistry

Section 1.5 Atomic Orbitals 19

To understand why nodes occur, you need to remember that electrons have both
particlelike and wavelike properties. A node is a consequence of the wavelike proper-
ties of an electron. Consider the following two types of waves: traveling waves and
standing waves. Traveling waves move through space; light is an example of a travel-
ing wave. A standing wave, in contrast, is confined to a limited space. A vibrating
string of a guitar is an example of a standing wave—the string moves up and down, but
does not travel through space. If you were to write a wave equation for the guitar
string, the wave function would be in the region above where the guitar string is
at rest and in the region below where the guitar string is at rest—the regions are of
opposite phase. The region where the guitar string has no transverse displacement is
called a node. A nodeis the region where a standing wave has an amplitude of zero.

An electron behaves like a standing wave, but—unlike the wave created by a vi-
brating guitar string—it is three dimensional. This means that the node of a 2satomic
orbital is actually a surface—a spherical surface within the 2satomic orbital. Because
the electron wave has zero amplitude at the node, there is zero probability of finding
an electron at the node.
Unlike satomic orbitals that resemble spheres,patomic orbitals have two lobes.
Generally, the lobes are depicted as teardrop-shaped, but computer-generated represen-
tations reveal that they are shaped more like doorknobs. Like the vibrating guitar string,
the lobes are of opposite phase, which can be designated by plus and minus
signs or by two different colors. (In this context, and do not indicate charge, just
the phase of the orbital.) The node of the patomic orbital is a plane that passes through
the center of the nucleus, bisecting its two lobes. This is called a nodal plane. There is
zero probability of finding an electron in the nodal plane of the porbital.

In Section 1.2, you saw that there are three degenerate patomic orbitals. The or-
bital is symmetrical about the x-axis, the orbital is symmetrical about the y-axis,
and the orbital is symmetrical about the z-axis. This means that each porbital is per-
pendicular to the other two porbitals. The energy of a 2patomic orbital is slightly
greater than that of a 2satomic orbital because the average location of an electron in a
2 patomic orbital is farther away from the nucleus.

z

y

x

y

x

z

y

x

2 px orbital 2 py orbital 2 pz orbital

z

pz

py

px

+ -

1 + 2 1 - 2

1 - 2

1 + 2

Degenerate orbitals are orbitals that

have the same energy.

vibrating guitar string upward displacement = the peak

pluck the

guitar string

node

downward displacement = the trough

+

−

or

2 p atomic orbital computer-generated

2 p atomic orbital

2 p atomic orbital

nodal plane nodal plane

+

−