Study of α-Particle Scattering.
The Rutherford Experiment
R. Thakrar
Laboratory Partner: F. Wahhab
Department of Physics and Astronomy
University College London
20th October 2009
This is the abstract.(style=Abstract)
1. Introduction
This experiment aimed to achieve the same results as the Rutherford scattering experiment. This
experiment was originally conducted by Ernest Rutherford in 1909 by investigating the angular
dependence of α-particle scattering from a gold leaf. The experiment will be used to verify that
the α-particle scattering takes place from a dense nucleus of positive charge, as Rutherford had
realised previously.1
α-particles are known now to be Helium nuclei, consisting of two protons and two neutrons.2 The
experiment is classically considered as a Coulomb Scattering between a massive nucleus and an
incident particle, considered to be both positive and point charges.
Scattering of these α-particles takes place on gold leaf – a piece of gold foil thin enough so that
scattering of α-particles from multiple gold nuclei can be ignored. As the gold particles are
heavy, the fraction of an incident parallel beam of intensity, I, scattered at an angle ϕ into a
detector normal to an area dS, at distance R from the scattering centre, is governed by Equation
(1) below.
Nt = number of atoms per unit volume in the
scattering foil (m-3)
t = thickness of foil (m)
do = collision diameter (m)
= ZZ’e/4πoT
= distance of closest approach of a particle in a
head on collision
Z = atomic number of scatterer
Z’ = atomic number of -particles
e = unit of electric charge
= 1.602 10-19 (C)
o = permittivity of free space
= 8.854 10-12 (Fm-1)
T = kinetic energy of -particles (eV)
The rate of their distributed flux also follows a general law stated in equation (2)
It is expected that n=4 in this experiment.
2. Method
2.1 Experimental Apparatus
A diagram of experimental apparatus being used in this investigation is shown in figure 1.
The container is connected to a vacuum pump so that it is possible for α-particles to penetrate
further than in air, where it can only go through a few centimetres.
The magnet is used to externally control the carriage to maintain its pressure. The carriage has the
source, gold leaf, and collimator slit on it, which can be rotated through various angles.
Note that when switching the apparatus off, a nozzle on the pump must also be slowly released to
avoid damaging the equipment.
2.2 Preliminary Experiment.
This experiment is carried out to find the optimum discriminator bias for the machine. The
apparatus is first set up as shown in Figure 1a and 1b. When the vacuum pump is turned on, the
valve on the pump is closed to lower the pressure. When the pressure is low, readings should
show on the signal processing unit connected to the detector. Readings of counts are recorded for
different values of the discriminator bias. The point of optimum bias is found to be the point at
which the values seem to plateau.
There may still be a residual low count due to background radiation after choosing the bias. To
accommodate for this additional error, a background measurement of radiation over 1000s is
determined with the vacuum pump switched off at angles ±90o.
2.2 Main Experiment: Dependence of Count Rate upon Angle of Scatter.
This part of the experiment measures the count rate at various scattering angles, both positive and
negative. For each measurement the time period of count should be chosen so that the precision
on the total count is large enough to be representative of the true count rate.
We assume that the decay of Americium 241 will be a Poisson distribution, the percentage error
can be given using equation (3). To decide how long to count for, a 10% precision was used,
giving N = 100. Hence for a 10% precision on values, over 100 counts must be taken for each
angle.
Each scattering angle is predicted to take a longer time for 100 counts to be reached. For
scattering angles greater than ±18o, the period for each count will be too large to be taken in the
time given for the experiment; hence only angles below ±18o will be calculated.
3. Results and Analysis
3.1 Preliminary Experiment
It was found that the time base setting on the counter had to be ranged between 10 and 1000 as
the angle increased.
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4. Conclusion
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5. References
1
E. Rutherford , "The Scattering of α and β Particles by Matter and the Structure of the Atom",
Philosophical Mag., volume 6, pp.21, 1909
2
http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/radact.html#c2