RUTHERFORD SCATTERING

Edan Bainglass

Jose Chavez

Kennedy Izuagbe

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

HOW IT ALL STARTED…

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

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

THE INITIAL EXPERIMENTS

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

()

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

b

RUTHERFORD'S THEORY (CONT.)

Rutherford showed that the number of alpha particles

scattered per unit area into the detector at scattering angle φ

is given by

𝑦= 𝑄𝑛𝑡𝑏2

16 r2 ∙ sin4𝜑2

or𝑦=𝑄𝑛𝑡

16 ( 𝑒2

4𝜋𝜖0 )2 𝑍1

2𝑍 22

𝑟2𝐾2 sin4𝜑2

y = number of scattered particles

Q = number of incident particles

n = atoms per unit volume

t = target thickness

Z1 = atomic number of alpha

particle

Z2 = atomic number of target

nucleus

K = kinetic energy of incident

particle

Φ = scattering angle

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 Particles. (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).