RUTHERFORD SCATTERING
Edan Bainglass
Jose Chavez
Kennedy Izuagbe
HOW IT ALL STARTED…

After his discovery of alpha particle emissions from a radioactive isotope of
Radon gas, for which he was awarded the 1898 Nobel prize in Chemistry,
Rutherford spent a considerable amount of time and effort into their investigation

As a student of J.J. Thomson at Cambridge University, Rutherford was familiar
with the Plum Pudding model and used it as the standard for his investigations
THE “PLUM PUDDING” MODEL

Shortly after discovering the electron in 1897, Prof. J.J. Thomson proposed
the “Plum Pudding” model

“We suppose that the atom consists of a number of corpuscles
moving about in a sphere of uniform positive electrification” – J.J.
Thomson
THE INITIAL EXPERIMENTS

Rutherford initially failed in counting individual alpha particles

Upon moving to the University of Manchester, he teamed up with Dr.
Hans Geiger, and with the use of Geiger’s apparatus, they began
recording individual scintillations of alpha particles
STRANGE RESULTS

The assumption, based on the Plum Pudding model, was that the alpha
particles will mostly pass right through the atom, with minimal deflection

Geiger originally calculated the most probable deviation of alpha
particles to be within 2°

Geiger suggested that the experiments should be given to a young student
named Ernest Marsden

Marsden returned to Geiger shortly after conducting the experiment with
strange results – some of the alpha particles had been deflected at a
“considerable” angle

Rutherford instructed Geiger and Marsden to perform further investigation
into the matter
GEIGER AND MARSDEN'S 1909 EXPERIMENT

Geiger’s Scintillation Method

Radium was used as a powerful, continuous source of alpha
particles

A low powered microscope was used to observe scintillations on a
ZnS screen

Different reflecting materials were used

Alpha particles were reflected unto the ZnS screen regardless of
the angle of incidence

About 1 in 8000 particles were reflected at angles greater than 90°
RUTHERFORD'S THEORY – THE NUCLEUS

Rutherford was shocked!!!

“It was almost as incredible as if you fired a 15-inch shell
at a piece of tissue paper and it came back and hit you.“
– E. Rutherford

In order to explain such events, Rutherford proposed a new atomic
model – one with a massive central charge confined to a very
small volume surrounded by an opposite and equal charge
uniformly distributed across the remainder of the atom

Rutherford later dubbed the central charge “the nucleus”
RUTHERFORD'S THEORY (CONT.)

Rutherford’s model explained both small and large deflections

As the ratio of the impact parameter p to the instantaneous
distance from the nucleus b decreases, the deflection
angle φ increases – stronger coulomb force (1/𝑟 2 )

b
Rutherford suggested that such large deflection angles most
likely occurred due to a single scattering event
p/b
10
5
2
1
.5
.25
.125
φ
5°.7
11°.4
28°
53°
90°
127°
152°
φ
y = number of scattered particles
Q = number of incident particles
RUTHERFORD'S THEORY (CONT.)
n = atoms per unit volume
t = target thickness
Z1 = atomic number of alpha particle

Z2 = atomic number of target nucleus
Rutherford showed that the number of alpha particles scattered
K = kinetic energy of incident particle
per unit area into the detector at scattering angle φ is given by
𝑦=

𝑄𝑛𝑡𝑏 2
16r 2 ∙ sin4
𝜑
2
or
𝑄𝑛𝑡 𝑒 2
𝑦=
16 4𝜋𝜖0
2
𝑍12 𝑍22
𝑟 2 𝐾 2 sin4
Φ = scattering angle
𝜑
2
Rutherford noted that the number of scattered particles is proportional to

The inverse square of the kinetic energy of the incident particle

The inverse 4th power of the sine of half the deflection angle

The square of the atomic number of the nucleus

The thickness of the target (for thin foils)
EXPERIMENTAL PROOF (1913)

Geiger and Marsden went on to prove their professor’s theory.
They tackled his four main conclusions by investigating the
change of the number of scattered particles with:

Variation of angle

Variation of thickness

Variation of atomic weight

Variation of velocity
THE EQUIPMENT
IN GOOD AGREEMENT

Geiger and Marsden found Rutherford’s theory to be correct

“It may be mentioned in anticipation that all the results of our
investigation are in good agreement with the theoretical deductions of
Prof. Rutherford, and afford strong evidence of the correctness of the
underlying assumption that an atom contains a strong charge at the
center of dimensions, small compared with the diameter of the atom”
– Geiger and Marsden (1913)

They concluded that it would be possible to calculate the probability of an
alpha particle being scattered through any angle under any specified
conditions
WHERE DID WE GO FROM THERE?

Rutherford’s theory and subsequent experiments provided a stepping stone
for future research into the structure of the atom

A few examples of such research:

Bohr’s stationary quantized energy states (1912) describing the
electron structure of the atom (later adjusted by quantum theory)

Rutherford’s discovery of the proton (1920)

The discovery of the neutron by James Chadwick (1932)

The discovery of quarks (1968, 1974, 1977, 1995)
CONCLUSIONS

Rutherford’s work was invaluable to science and allowed us to have a
clearer picture of the inner workings of our world

It is interesting to note that similar to the strange results of his team,
Rutherford turned out to be quite the anomaly, as his greatest
achievements – the theory of the nucleus, the discovery of the proton – all
came after he had already been awarded the Nobel prize - a first!

The methods used by Rutherford and his team are still used today to further
investigate the atomic world
REFERENCES

1. E. Rutherford, F.R.S.*, The Scattering of and β Particles by Matter and the
Structure of the Atom, Philosophical Magazine. Series 6 vol. 21, p. 669-688
(1911).

2. H. Geiger and E. Marsden, On a Diffuse Reflection of the
(1909).

3. H. Geiger and E. Marsden, Assistants Paper. Philosophical Magazine 25. p
605-623 (1913).

4. J.J. Thomson, On the Structure of the Atom: an Investigation of the
Stability and Periods of Oscillation of a number of Corpuscles arranged at
equal intervals around the Circumference of a Circle; with Application of
the Results to the Theory of Atomic Structure. Philosophical Magazine. Series
6, Volume 7, Number 39. p. 237-265. (1904).
Particles.