# Rutherford scattering

Rutherford Scattering was a phenomonon observed by Ernest Rutherford in the 1911 which led to the development of the orbital theory of the atom.

At the time the atom was thought to be a sort of plum pudding, with the electrons and protons mixed together like the ingredients of a cake. Rutherford conducted an experiment whereby he he shot a beam of alpha particles (electrons) at layers of gold leaf only a few atoms thick. If the plum-pudding model was correct the vast majority of electrons would get stuck in the atoms, while some would get through.

The results were intriguing. The majority of electrons actually made it through whereas some were deflected by very large angles (over 90o). Rutherford concluded that the majority of the mass was concentrated in a minute, positively charged region orbited by electrons. When an negative electron became sufficiently close to the nucleus it was repelled strong enough to rebound at high angles. The small size of the nucleus explained the small number of electrons that were repelled in this way. He showed using the method below that the size of the nucleus was about 10-14 m large.

For cases when p = 0 (a head on collision), all the kinetic energy (.5mu2) of the electron is turned in to potential energy, and the particle is at rest. The distance from the centre of the electron to the centre of the nucleus (b) is approximately then the radius.

Using the inverse square law can be applied to the charges on the electron and nucleus one can write:

``` .5mu2 = (1/4*pi*e0)*(q1q2/b)
```

Rearranging:

``` b = (1/4*pi*e0)*(q1q2/.5mu2)
```

For an alpha particle:

``` m (mass) = 6.7*10-27 kg
q1 = 2*(1.6*10-19) C
q2 (for gold) = 79*(1.6*10-19) C
u (initial velocity) = 2*10-7 ms-1
```

Substituting these in gives the value of about 2.7*10-14 m.