The scale of the matter
in different levels
The experimental technique
of deep inelastic scattering
has revealed to understand
the most basic structure of
matter
1.6 Atomic structure:
• The “plum-pudding” model (ca. 1900
Thomson) imagined electrons embedded in a
jelly-like positive medium.
• Rutherford proposed a “planet model” or
Rutherford model
Rutherford, Geiger & Marsden found that particles fired at a thin gold foil occasionally
scattered backwards.
Discovery of the electron
• In the late 1800s several experiments were
performed on electrical discharges in gases at
low pressure.
• It was established that a stream of some kind
of “rays” – called cathode-rays – was emitted
by any electrode at high negative potential in a
vacuum tube.
– What were these rays?
Gas discharge tube
Discovery of the electron
J. J. Thomson clarified the situation with a decisive
experiment.
Particles have negative charge
• By measuring the deflection of these particles Thomson
showed that all the particles have the same q/m ratio.
• Thomson also showed that particles with this q/m ratio
can be obtained using any material as source –
These particles – now called electrons – are a fundamental
constituent of matter.
Thomson’s e/m experiment
• Thomson found that in his experiment, the speed
of the particles was extremely high – ~ 1/10 c
• Value of q/m = 1.7588  104 C/kg
Thomson was able to show that this new particle
– the electron – with its absolutely characteristic
charge-to-mass ratio was a constituent of every
substance that he was able to use as a cathode
material.
Millikan’s “Oil-drop” Experiment
• Millikan’s oil-drop experiment demonstrated that electric charge is
quantized and transferred in integral multiples of e.
Millikan provided first crude measurement of e.
We know now: e = 1.6022  10-19 C.
m = 9.109  10-28 g.

  
dv
Fm
 e[E  ( v  B)]
dt
It was supposed that the
positive charges were heavier
than the electrons –
The hydrogen ion turned out to
be 1836 times heavier than the
electron.
Millikan’s “oil-drop” experiment
Experimental arrangement of Millikan. The oil droplets, which are formed by
the atomiser, can be charged or discharged by irradiation with x-rays.
Plum-pudding model
• Atomic radii: R ~ 1 Å = 10-10 m
Thomson’s atomic model:
Atom has to be electrically neutral.
• Thomson proposed an atomic model in which electrons
were embedded in a massive matrix of positive charge
filling a volume of roughly 1 atomic diameter (~ 1 Ao).
This model is called the “plum-pudding” model in which
the electrons are analogous to raisins in a plum pudding.
electron
R ~ 10 -10 m
e
e
e
e
R
• Electrons are almost point charges
• Calculations based on classical
E&M gives ro = e2/mc2
• Radius of electron  2.8 X 10-15 m
e
Positively charged
matter
The nucleus of the atom
Cloud chamber pictures
wall
Cloud chamber
The track of
alpha particle
Cloud chamber photograph of the track of an alpha particle, by wilson. The
particle passes through several cm of air without noticeable deflection. At the end
of the track, we see two deflections; at the second, we can also see the short track
of the target nucleus, which was accelerated to the right by the collision.
Cloud chamber pictures
H gas
He gas
deflection
Cloud chamber photograph of alpha particles. Left, the chamber gas is hydrogen.
The alpha particle is only slightly deflected from a straght-line track, while the
hydrogen nucleus recoils sharply off to the left. Right, it is helium. The angle
between the tracks of the alpha particle and the recoiling nucleus after the
collision is 900, since the two particles have the same mass.
Rutherford model of the atom
• The most direct way of finding out what’s
inside a fruitcake is to put a finger into it -– A method similar to that used by Geiger
and Marsden in 1911.
• At the suggestion of Rutherford, they used
as probes fast -particles emitted by certain
radioactive elements (-particles are helium atoms that have lost
2 electrons – charge +2e)
Rutherford scattering experiment
-particles
Microscope
Zinc sulphide screen (gives off
a green flash when struck by )
Radioactive substance
that emits -particles
Thin metallic foil
• It was expected that  would go straight through the foil
without deflection (follows from Thomson’s model)
• With only weak electric forces exerted on them  ought to
deflect only slightly – 1o or less.
• G&M found that while most  were not deviated much, some
scattered through very large angles.
Some even scattered backwards!
Scattering by thin gold foils (on glass)
Measured a scattering through materials
Rutherford and Geiger first measured
scattering of a particles through the foils.
With the thinnest foils, scattering was
only 1 or 2 degrees.
Undergraduate experiment for Ernest
Marsden: “see if any alpha particles are
scattered backward.”
To Rutherford’s great surprise, there
were indeed alphas scattered backward.
He later said: “It was as incredible as if
you fired a 15” shell at a piece of tissue
paper and it came back and hit you!”.

Scattering of  rays by an atom
Setting of the experiment
Most of the  particles are pass
through straight, part of them are
scattered in large angles, even in
backward.
Results of Rutherford scattering
N
1

sin
2
4
Scattering angle 
The experimental results of Geiger and Marsden for the Rutherford scattering of 
particles by a gold foil. The scattering rate N is plotted as a function of the scattering
angle . The solid curve represents the theoretical function for Coulomb scattering.
Rutherford model of the atom
• Rutherford found – only way to explain results is to picture the
atom as being composed of a tiny nucleus with the electron
some distance away:
-
Within an atom being mostly empty
space, most  are undeflected.

+
-
Rutherford’s model
But, when  comes near nucleus, intense electric
field cause it to be scattered through large
angles – (E ~ 1021 V/m)
Rutherford model of the atom
• All the atoms of any one element were found to have
the same unique nuclear charge.
— This charge increased regularly from element
to element in the periodic table.
• Nuclear charge always turned out to be multiples of
+e the number Z of the element.
Ordinary matter, then, is mostly empty space.
By considering only the Coulomb interaction
between the incident  and the target nucleus,
Rutherford calculated the scattering counts and
obtained results which agreed remarkably well
with experiments.
Rutherford, Ernest (1871-1937)
New Zealander-English physicist who was born in Nelson, New
Zealand. Rutherford is best known for devising the names alpha,
beta, and gamma rays to classify various forms of "rays" which
were poorly understood at his time.
Rutherford suggested that the simplest possible rays must be those
obtained by hydrogen and that these must be the fundamental
positively charged particle, which he dubbed the proton in 1914.
In 1917, he passed alpha particles through a gas of nitrogen and
occasionally observed scintillation of hydrogen impacting on his
screen. He concluded that the alpha particles were knocking
protons out of the nitrogen atoms, and thus that he had made the
first observation of nuclear reactions.
Rutherford's image appears on New Zealand's $100 note, that
country's largest denomination of paper currency. One particularly
memorable quote attributed to Rutherford is "All science is either
physics or stamp collecting“.
In 1908 Rutherford was awarded the Nobel Prize – for Chemistry! The award
citation read – “For his investigations into the disintegration of the elements and
the chemistry of radioactive substances.”
Rutherford scattering
 2 Ze 2 r
The repulsive Coulomb force: F 
40 r 2 r
Trajectories for Rutherford Scattering
12
10
8
6
4
 particle
2
-θ0
b
-4
-2
2
4
6
8
Derivation of Rutherford’s scattering formula
Scattering angle
 particle
impact parameter
Rutherford's model enables us to derive a formula for the angular
distribution of scattered -particles. Basic Assumptions:
a) Scattering is due to Coulomb interaction between -particle and positively
charged atomic nucleus.
b) Target is thin enough to consider only single scattering (and no shadowing)
c) The nucleus is massive and fixed. (This simplifies the calculation, but it could
be avoided by working in the centre of mass frame).
d) Scattering is elastic.
Relation between b and 
k
b
cot( / 2),
2
mv 0
2Ze 2
k
40
Rutherford formula
The incident  particles with
impact parameters in the
range b to b+db are deflected
into the range of angles  to
-d.
Differential cross section da: da  2bdb
da 
Z 2e 4
40  m v
2
2 2
0
4
sin (

2
d ( 1 )
)
The Rutherford formula and the
experimental results
The Rutherford formula has been experimentally tested with
great care. Keeping the solid angle d constant, the sin-4(/2)
law is found to be excellently reproduced in the counting rate.
Even with the alpha particles of energy 5MeV and scattering
angle of 1500, no deviations from the Rutherford formula are
found; this corresponds to an impact parameter of 6×10-15 m. In
this region, only the Coulomb potential of the nucleus has a
measurable effect on the alpha particles. The nucleus radius is
thus R < 6×10-15 m.
From experiments with different foil materials, the nuclear
charge Z can be determined. The experiments of Chadwick
(1920) verified that Z is identified with the position of the
element in the periodic table.
The anomalous Rutherford scattering
The scattering of very fast alpha particles ( E > 6MeV) at
large angles , i.e., with small impact parameters b — nearly
central collisions, clear deviations from the Rutherford
formula, the sin-4(/2) law is never obeyed.
The alpha particles approach the nuclei so closely, the shortrange interaction force becomes more effective than
Coulomb force.
The nuclear force
An alpha particle, which approaches a nucleus from outside
the atom, is acted on at first only by the repulsive Coulomb
potential. If it approaches the nucleus sufficiently closely, it
will also be acted upon by the attractive nuclear force.
What is meant by nuclear Radius
Nuclear force and Coulomb
potentials
The nuclear Radius: the distance at which the
effect of the nuclear potential is comparable to
that of the Coulomb potential.
The empirical result of the nuclear Radius R and
the mass number A:
R = (1.3 ± 0.1)A1/3 · 10-15 m
Numerical examples for A = 12 and A = 208:
R(126C )  2.7  10 15 m,
15
R( 208
Pb
)

7
.
1

10
m
82
Scattering processes play an important role in
nuclear and elementary particle physics, in the
investigation of the internal structure of nuclei and of
certain elementary particles.
For example, Hofstadter was granted the Nobel prize
in 1961 for his scattering experiments using fast
electrons ( 109 eV) on protons and neutrons. From the
angular dependence of the scattering intensity, he was
able to obtain information about the inner structure of
the proton and of the neutron.
Homework:
Pp48, problems 4.2, 4.3, 4.6, 4.8