Page 37 - Modern physical chemistry

26 Structure in Molecules and Atoms

where A. is the wavelength. It has the direction of the beam.
Particles with a definite momentum may be obtained by passing a heterogeneous
beam through a velocity selector. This may be a mechanical device consisting of a series
of rotating discs containing openings that line up for the desired velocity. Or, when the
particles are charged, the selector may employ a crossed electric and magnetic field.
Alternatively, charged particles may be accelerated from approximate rest by a mea-
sured voltage increment V. If+e is the charge on the particle, the loss of potential energy,
and the gain in kinetic energy, during the acceleration is ±eV. Parameter e may be the
magnitude of the charge on an electron or a small multiple of it. So a convenient unit of
energy is the kinetic energy acquired by an electron on moving freely through a voltage
rise of one volt, the electron volt (eV).
When m is the mass of the particle and p its momentum, the gain in kinetic energy is
2
L=±eV, [2.18]
2m

as long as Newtonian mechanics is applicable.

Example 2. 1
Relate the wavelength of a homogeneous electron beam to the voltage accelerating
the electrons.
From equation (2.18), we have

112
p= 2meV ) .
(
Substituting this expression into the de Broglie equation
h
p=-
A
obtained from (2.16) and (2.17), and solving for the wavelength yields
h
A=----
(2mevf/2

Now introduce accepted values of the fundamental constants to get
A = 6.6261 x 10- 34 J s 1 = 12.264 x 10-10 V- 1I2 m = 12.264 V- I12 A.
[ ( )( )J 1I2 V1l2
2 9.1094 x 10- 31 kg 1.6022 x 10- 19 C

This can be rewritten in the form
112
A = 15~41 ] A.
[

2.4 Diffraction by Randomly Oriented Molecules
Bond distances and bond angles can be obtained from diffraction data. In a common
setup, a homogeneous beam of particles passes through a low pressure jet of the material.