E X P E R I M E N T K
Keele University Physics/Astrophysics Laboratory
School of Physical and Geographical Sciences Experimental Scripts
76
Electron diffraction and the measurement of Planck’s constant
1. Introduction
It is well known that if light is focused on a diffraction grating of spacing d, then the light will
be diffracted through some angle θ given by the equation λ = dsin θ where λ is the wavelength of the
light. In 1926 Louis de Broglie suggested that particles (in this case electrons) should have “wave-like”
properties so that the electron will have an effective wavelength which would be inversely
proportional to the electron's momentum. This is known as the “de Broglie Hypothesis” and this
experiment will test this theory.
The diffraction grating spacing required to diffract electrons is approximately 10-10 m, and
therefore the ideal way to observe the effect is to diffract the electrons using a crystal lattice where the
lattice spacing is ≈ 10-10 m. In this experiment, an electron gun is used which focuses an electron
beam at a graphite target. The electrons are accelerated through a potential difference of up to 5 kV
on to the graphite target and then diffracted on to a luminescent screen.
Two concentric rings will be observed. This is because the graphite lattice has a structure such
that there are two effective “grating spacings”. The inner ring corresponds to a spacing of d = 0.213
nm and the outer ring corresponds to d = 0.123 nm.
Theory
The de Broglie Hypothesis is,
mv
h
(1)
where λ = wavelength of electron
h = Planck’s constant
v = velocity of electron
If the electron has been accelerated through a potential difference Va, then the kinetic energy gained is
eVa (e = electronic charge).
Thus:
2
2
1mveVa
m
eV
va
2
(2)
Substituting (2) into (1):
nm
23.1
2aa VmeV
h
(3)
Thus a measure of λ as a function of Va can be investigated to test equation (3) and verify the
hypothesis.
