Page 266 - Essentials of physical chemistry

228 Essentials of Physical Chemistry

e – e –

e – e –
e –
e –
e – e –

e – e –

Ѳ
Ѳ
{1, 1, 1} plane
2.034 Å
{1, 1, 1} plane
nλ = d sin Ѳ
d = 2.034 Å
~
Ѳ – – 55°
λ = 1.67 Å
E = 54 eV
FIGURE 10.14 ‘‘Half-Bragg’’ nl ¼ d sin (u) diffraction of 54 eV electrons in a beam perpendicular to the
{1, 1, 1} plane of Ni observed by Davisson and Germer [10]. It is clear that Davisson and Germer used
nl ¼ 1d sin (u) on page 723 of their paper.

l 1
1
so u ¼ sin . Then u ¼ sin (0.820338608) ¼ 55.11878 roughly in agreement with the experi-
1d
mental result using nl ¼ 1d sin(u)! Some of the curves shown in the original paper can be interpreted
as peaks at angles slightly larger than 508 while others show the peaks at almost exactly 508. Since
modern technology uses such scattering to characterize surfaces, the wave diffraction of electrons has
been established beyond any uncertainties in the original experiment (Figure 10.15). Because the raw

G
T
F

C
P

FIGURE 10.15 A cross section view of the original Davisson–Germer apparatus. The Ni crystal is the target
‘‘T,’’ ‘‘G’’ is the electron gun and ‘‘C’’ is the collector, which can travel on a curved track to measure the angle
of scattered electrons entering the collector. ‘‘F’’ is a heated tungsten filament, which emits thermal electrons as
the source. ‘‘P’’ is the electrical potential wire. Note the width of the entrance to the detector cup seems to be at
least 28 of arc leading to some uncertainty of the angle by a small amount. (Reprinted with permission from
Davisson, C. and Germer, L.H., Phys. Rev., 30, 705, 1927. Copyright 1927 by the American Physical Society.)