Page 267 - Essentials of physical chemistry

Early Experiments in Quantum Physics 229

50°

55°

35°
Collector current 45° 60°
40°

65°

70°
V
35 40 45 50 55 60 65 70 75
Bombarding potential
FIGURE 10.16 Raw data from the Davisson–Germer experiment showing detection of scattered electrons at
various angles of the collector versus the energy of the electron beam. A 558 angle calculated in the text is very
close to the simple protractor measurement compared to the 508 peak shown here for a beam of 54 V. Note the
acceptance width of the detector cup surely is wider than 18 and no uncertainty is given for how close the {1, 1, 1}
plane was oriented to be perpendicular to the incident beam so the calculation with the modern cell constant
for Ni changes the angle slightly but it is still within the variation of the data shown. (Reprinted with permission
from Davisson, C. and Germer, L.H., Phys. Rev., 30, 705, 1927. Copyright 1927 by the American Physical
Society.)

data was presented in an unusual way, we also show the diagram of the original equipment with the
sliding arc track for the detector cup relative to the electron beam from the ‘‘gun.’’
The surface of the nickel block was oriented so that the {1, 1, 1} surface was exposed and a very
strong peak was observed using a collector cup with a galvanometer to measure the diffracted
electrons and many careful checks were made to test the energy of the scattered electrons compared
to random background scattering, and the 1927 paper [10] is an amazing example of thorough
scientific work. In Figure 10.14 we sketch the path of electrons incident perpendicular to the surface
of the target block with the spacing of 2.034 Å between the Ni atoms arrayed in the {1, 1, 1} plane.
Although Davisson and Germer used a {1, 1, 1} spacing of 2.18 Å to arrive at a 508 angle for the
54 V beam compared to a modern value of 558 using a spacing of 2.034 Å (Figure 10.16), the
observation of the second large diffraction at 65 V is a very convincing demonstration of diffraction
(Figure 10.17). The most interesting thing about the experiment is that the beam is directly at the
surface of the block perpendicular to the surface and the fact that the diffraction follows what might
be called a ‘‘half-Bragg’’ rule of nl ¼ 1d sin(u).
There are two important results from the Davisson–Germer experiment. Foremost is the agree-
ment with the De Broglie equation and that is the overwhelming immediate payoff of the result. In
fact, L. De Broglie was awarded the Nobel Prize not long after in 1929! Clinton Davisson (1881–
1958) was awarded the Nobel Prize for this work later in 1937. For our later chapters, this is also the
foundation of ‘‘wave mechanics,’’ the Schrödinger equation, quantum chemistry, molecular orbital
theory, and modern spectroscopy. It really is that important to prove particles have wave properties
or at least behave as if there is some sort of common wave behavior in the mathematics. Having said
that, one might think the experiment is over and done with, but reading the full 1927 paper shows
that a number of additional diffraction peaks were assigned to gas molecules absorbed on the Ni
surface. Thus a second more recent use of this effect is the study of surface chemistry with improved
methods of simultaneous detection of multiple diffraction spots similar to x-ray diffraction.