_
62
'
3.
WAVELENGTH OF THE
due to an acceleration by 1000 volts. If we are content to know
the position of the electron at a given instant to within one millimeter only (Ax = 0.1 cm.), then We may, if our tools are suiciently
reried, measure the Velocity to within about 728 centimeters
per
second (Av = 728).
Thus
the
of the
electron,
-1.88
.
X 109 centimeters per second, may be determined With
excellentaccuracy, at the expense
of the accuracy
in position determination.
If, however, we wish to know to within one angstrom
where to nd the electron at a given moment, then, from equation
.
.
3—14, it is impossible to state the velocity with which the electron
is travelling, since the uncertainty in its value is greater than the
quantity itself. Conversely, if a given experiment requires that
the velocity be measurable to within a certain degree of accuracy,
then the position of the electron can never be computed more
accurately than the limit set by equation 3—14.
.
3—11.
The Wave Nature of Heavier Particles.—Hydmgen
molecules, helium and hydrogen atoms,7 as well as protons8 (the
nuclei of hydrogen atoms), have been diffracted from crystals in
a manner similar to that for electrons, demonstrating their wave
'
nature.
For example, a narrow beam of hydrogen atoms has been
directedupon a lithium uoride crystal. The reected atoms
were detected by their action upon a molybdenum trioxide sur—
face.
The colored streaks produced upon this detecting material
after—suitable exposure
to the atoms were shown to be the di“rac4
tion pattern produced by the two dimensional grating formed by
'
the rows of lithium and uorine atoms on the surface of the crystal.
From the pattern and the known separation of the atoms of
crystal (x—r'ay analysis), the Wave—lengths of the atoms were côm'
=
puted and found to agree With the de Broglie wave-lengths,
7\" ‘=Ï ]z/m0, for‘ particles of mass equal to that of
,
atom
travelling at the velocity of the atoms in the inCident
…
_
_
beamThe Velocities were those of thermal motion,as given by
_
-ïtlîe kinetic theory for the temperature of the source and were d13»
'
‘tibutedË‘ab‘out-a'mostprobablè value according to the usual MaX—
The
'
atoms at room
accelerated by 15,000
andbY‘m‘mV©1tshave wavelengthsofooœs
00014 ang
62
'
3.
WAVELENGTH OF THE
due to an acceleration by 1000 volts. If we are content to know
the position of the electron at a given instant to within one millimeter only (Ax = 0.1 cm.), then We may, if our tools are suiciently
reried, measure the Velocity to within about 728 centimeters
per
second (Av = 728).
Thus
the
of the
electron,
-1.88
.
X 109 centimeters per second, may be determined With
excellentaccuracy, at the expense
of the accuracy
in position determination.
If, however, we wish to know to within one angstrom
where to nd the electron at a given moment, then, from equation
.
.
3—14, it is impossible to state the velocity with which the electron
is travelling, since the uncertainty in its value is greater than the
quantity itself. Conversely, if a given experiment requires that
the velocity be measurable to within a certain degree of accuracy,
then the position of the electron can never be computed more
accurately than the limit set by equation 3—14.
.
3—11.
The Wave Nature of Heavier Particles.—Hydmgen
molecules, helium and hydrogen atoms,7 as well as protons8 (the
nuclei of hydrogen atoms), have been diffracted from crystals in
a manner similar to that for electrons, demonstrating their wave
'
nature.
For example, a narrow beam of hydrogen atoms has been
directedupon a lithium uoride crystal. The reected atoms
were detected by their action upon a molybdenum trioxide sur—
face.
The colored streaks produced upon this detecting material
after—suitable exposure
to the atoms were shown to be the di“rac4
tion pattern produced by the two dimensional grating formed by
'
the rows of lithium and uorine atoms on the surface of the crystal.
From the pattern and the known separation of the atoms of
crystal (x—r'ay analysis), the Wave—lengths of the atoms were côm'
=
puted and found to agree With the de Broglie wave-lengths,
7\" ‘=Ï ]z/m0, for‘ particles of mass equal to that of
,
atom
travelling at the velocity of the atoms in the inCident
…
_
_
beamThe Velocities were those of thermal motion,as given by
_
-ïtlîe kinetic theory for the temperature of the source and were d13»
'
‘tibutedË‘ab‘out-a'mostprobablè value according to the usual MaX—
The
'
atoms at room
accelerated by 15,000
andbY‘m‘mV©1tshave wavelengthsofooœs
00014 ang