Page 105 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:36 9in x 6in b985-ch08 Elementary Physical Chemistry

90 Elementary Physical Chemistry

de Broglie suggested that a similar expression applies to a particle moving
with a velocity v
λ = h/mv = h/p (8.3c)

In other words, a particle moving with a velocity v has a wave associated
with it.
The de Broglie hypothesis was confirmed a few years later by Davisson
and Germer, who analyzed diffraction patterns of electrons by crystals and
observed interference patterns similar to inference by light.
For example, a person weighing 70 kg moves with a velocity of v =
1m s −1 . By the de Broglie equation, the wavelength is
2 −1
λ =6.626 × 10 −34 m s /70 kg m s −1 =9.5 × 10 −36 m.
The new ideas that were introduced next were so strange and weird that
only the most gifted scientists could understand them. What finally emerged
was not just a generalization of classical theories but an entirely new
framework, different conceptually and philosophically from the old theories.
Three different formulations of the new theory emerged between 1925
and 1927. They are referred to as

(1) Wave-Mechanics (Schr¨odinger)
(2) Matrix Mechanics (Heisenberg, Born, Jordan)
(3) Quantum Theory (Dirac)

The three formulations looked mathematically different, but turned
out to be equivalent. Following are some anecdotal details of the new
developments.

(1) There is a story that Debye at Zurich Polytechnic said to Schr¨odinger
(a younger faculty member), “Erwin, since you are not doing anything
useful these days why don’t you find out what de Broglie is up to and
tell us about it.” Schr¨odinger did that. It became clear to Schr¨odinger
that if there was such a thing as matter waves, there must be a wave-
equation describing those waves, analogous to the Maxwell equations
describing electromagnetic waves. Schr¨odinger set out to discover the
matter wave-equation.
(2) Heisenberg went to Helgoland trying to get rid of a severe bout of
hay-fever. There he worked on problems involving quantum theory.
Rather than focusing on de Broglie’s ideas, as Schr¨odinger did, he