For the electron: 2.43
10 ^10 m or 2.43 Å
The de Broglie wavelength of the automobile is unnoticeable even using
modern methods. The de Broglie wavelength of the electron is similar to that
of X rays, which are certainly noticeable under the right conditions.De Broglie’s insight and the Davisson-Germer experiment ultimately pointed
out that matter has wave properties. For large pieces of matter, the wave prop-
erties can be ignored, but for small pieces of matter like electrons, they cannot.
Because classical mechanics did not consider matter as waves,it was inadequate
to describe the behavior of matter.
9.11 Summary: The End of Classical Mechanics
By 1925 it was realized that the classical ideas that described matter didn’t work
at the atomic level. Some progress—Planck’s quantum theory, Einstein’s appli-
cation of quantum theory to light, Bohr’s theory of hydrogen, de Broglie’s re-
lationship—had been made, but it was all very specific and not generally ap-
plied to atoms and molecules.
It took a generation for new thinkers, exposed to the new and fantastic ideas
of the last quarter century, to propose the new theories. It has been debated
philosophically whether new thinkers were required; would older scientists still
be bound by the old theories and be unable to come up with totally new ideas?
In 1925–1926, the German physicist Werner Heisenberg and the Austrian
physicist Erwin Schrödinger independently and from different perspectives
published initial works announcing the formation ofquantum mechanics,a
new way of thinking of electrons and their behavior. From their basic argu-
ments, an entirely new concept of atoms and molecules was constructed. Most
importantly, this picture of atoms and molecules survives because it answers
the questions about atomic and molecular structure, and it does so in a more
complete way than any theory before or since. As with most theories, quantum
mechanics is based on a set of assumptions called postulates. Some of these
postulates seem, and certainly seemed to fellow scientists in 1925, a totally new
way of thinking about nature. But as one concedes the success of quantum me-
chanics, it becomes easier to accept the postulates as factual and then try to
come to grips with what they mean.
Before we consider quantum mechanics itself, it is important to understand
that we will be applying quantum mechanics to atomic and molecular behav-
ior, not to the behavior of large macroscopic objects. Ordinary, classical me-
chanics can be used to understand the behavior of a baseball, but not an elec-
tron. It is completely analogous to using Newton’s equations to understand the
velocity of a car going 100 km/hr, but using Einstein’s equations of relativity
to understand the velocity of a car at near the speed of light. Although one
could use relativity equations to model very slow speeds, it is impractical
within the limits of measurement. So it is with quantum mechanics. It applies
to all matter, but it is not needed to describe the behavior of something the size
of a baseball. By the end of the nineteenth century, scientists began probing
matter the size of atoms for the first time, and their observations couldn’t be
explained using classical mechanics. That’s because they were assuming that
6.626
10 ^34 Js
(9.109
10 ^31 kg)(3.00
106 m/s)9.11 Summary: The End of Classical Mechanics 269