Rutherford Scattering
1 Introduction
In 1911 Ernest Rutherford discovered the atomic nucleus by scattering α-particles (nuclei of He-
lium atoms) from a gold foil and observing that some of the α-particles were scattered at backward
angles. These results were in startling contradiction with J. J. Thomson’s popular "plum pudding"
model in which the atom is a spherically shaped mass of positive charge in which negative elec-
trons are embedded. Rutherford concluded that these observations, however, were consistent with
a new model in which all of the atom’s positive charge and nearly all its mass are concentrated in
a small region.
This was the first demonstration of how scattering experiments can be used to study atomic struc-
ture, and was the birth of nuclear and particle physics. Today’s high energy physics experiments
employ these techniques to learn about the structure of known subatomic particles and to discover
new particles.
In this lab we will use the 1-MV Pelletron accelerator in room N008 of the Science and Engineering
Center to scatter α-particles from thin foils. By measuring the kinetic energies and angles of the
scattered α-particles and applying conservation of momentum and energy, we will infer the masses
of the target nuclei.
2 Theory
Consider a particle of mass mwith initial momentum −→
pithat collides with another particle of mass
Mthat is initially at rest, as shown in Figure 1. The incident particle scatters at an angle θwith a
final momentum −→
pfwhile the target particle recoils at an angle φwith a momentum −→
P.
From conservation of momentum we have
−→
pi=−→
pf+
−→
P.(1)
Using the momentum diagram in Figure 2, we can write an expression for the square of the mo-
mentum of the recoiling target particle
P2=−→
pi−−→
pf2=p2
i+p2
f−2pipfcosθ.(2)
Assuming the collision is elastic, we can apply conservation of kinetic energy and write
Ki=Kf+K(3)
where Ki,Kf, and Kare the kinetic energies of the incident, scattered, and recoil particles, re-
spectively. Inserting the expression for the kinetic energy of a particle in terms of its momentum,
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