54
3. ' WAVE-LENGTH OF THE ELECTRON
'
the comparatively large crystal. Each unit cell, in turn, ismade
up
of atoms arranged in some geometrical pattern, such as a cube
.
or a distorted parallelepiped. Standing
at the side of an orcha‘rd,
one can see rows of trees extending in various directions, at various
angles. Similarly, if the crystal could be suiciently enlarged,
’
one would see rows of atoms on its surface, forming the lines of a
two-dimensional grating and also, inside, one would see various
lattice planes, populated by atoms, in a three—dimensional array. _
In certain directions the perpendicular distance between the planes
'
wouldbe comparatively large and in others it would be small. In
some of the planes the atoms would
be close'to one another and
in other planes the atomic population would be small.
There is a particular angle at which X—rays of a given wave—
.
length will be reected in appreciable intensity from the lattice
planes in a given surface of a given crystal. This angle,* 6, is such
that the X-ray waves Which are reected from the various lattice
planes have path—differences equal to an integral multiple (71) of
the wave-length )\. Then, the various reected waves combine,
…
.
crest for crest, to reinforce each other.
At other angles, destructive interference occurs and the intensity of the X—ray beam is
reduced to zero.
Bragg has expressed‘this phenomenon of selective
'
reection by the equationî
_
nx = 20] sin 9.
(3—8)
'
From this it may be seen that the abscissae (71) in the lower curve
‘
of gure 3—2, are proportional to the reciprocal of the wave—length
of the x—rays.
_
3—5.
The Diffraction of Electrons.—There _is no a priori
reason to suspect that electrons, when treated as charged particles,
Should be readily reected from the electrically charged constitu—
ents. of the atoms in lattice planes when travelling at a particular
,
'
velocity
and not at another velocity. Yet this phenomenon was
.
established by the experimental work of Davisson'and Germer, as
illustrated in gure 3—2. On the other hand, if the electronsare
.
thought of as waves whose length is comparable to the spacing
…
between the lattice planes:and which varie3with their speed, then
j>$‘Ç'lectivereeCtion should lie expected, The de “Broglie equation, ,
‘
equation is derived in the x_-ray chapter;
_
-
—
3. ' WAVE-LENGTH OF THE ELECTRON
'
the comparatively large crystal. Each unit cell, in turn, ismade
up
of atoms arranged in some geometrical pattern, such as a cube
.
or a distorted parallelepiped. Standing
at the side of an orcha‘rd,
one can see rows of trees extending in various directions, at various
angles. Similarly, if the crystal could be suiciently enlarged,
’
one would see rows of atoms on its surface, forming the lines of a
two-dimensional grating and also, inside, one would see various
lattice planes, populated by atoms, in a three—dimensional array. _
In certain directions the perpendicular distance between the planes
'
wouldbe comparatively large and in others it would be small. In
some of the planes the atoms would
be close'to one another and
in other planes the atomic population would be small.
There is a particular angle at which X—rays of a given wave—
.
length will be reected in appreciable intensity from the lattice
planes in a given surface of a given crystal. This angle,* 6, is such
that the X-ray waves Which are reected from the various lattice
planes have path—differences equal to an integral multiple (71) of
the wave-length )\. Then, the various reected waves combine,
…
.
crest for crest, to reinforce each other.
At other angles, destructive interference occurs and the intensity of the X—ray beam is
reduced to zero.
Bragg has expressed‘this phenomenon of selective
'
reection by the equationî
_
nx = 20] sin 9.
(3—8)
'
From this it may be seen that the abscissae (71) in the lower curve
‘
of gure 3—2, are proportional to the reciprocal of the wave—length
of the x—rays.
_
3—5.
The Diffraction of Electrons.—There _is no a priori
reason to suspect that electrons, when treated as charged particles,
Should be readily reected from the electrically charged constitu—
ents. of the atoms in lattice planes when travelling at a particular
,
'
velocity
and not at another velocity. Yet this phenomenon was
.
established by the experimental work of Davisson'and Germer, as
illustrated in gure 3—2. On the other hand, if the electronsare
.
thought of as waves whose length is comparable to the spacing
…
between the lattice planes:and which varie3with their speed, then
j>$‘Ç'lectivereeCtion should lie expected, The de “Broglie equation, ,
‘
equation is derived in the x_-ray chapter;
_
-
—