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This is a copy of what was written in Rutherford's laboratory notebook for the alpha scattering experiment. This is where he realises what the results mean and calculates a value for the size of a gold nucleus.
Theory of deflections of a-particles through angles large compared with small scattering.
Suppose atom of material to consist of sphere with central point charge +Ne where is e is ionic charge surrounded by a sphere of radius R in which a negative charge -Ne (...) is uniformly distributed. Atom is neutral.
Consider passage of atom of mass m carrying a charge E moving with velocity vo. Suppose charge concentrated at point. If alpha is fired straight for centre, it will lose it's velocity at a distance b from centre given by
1/2mvo2 = NeE/ b
since NeE / b is potential energy of (...) charge(...)
therefore b = 2NeE / mvo2
Consider value of b. Take N for atom of gold 200 as found for small scattering.
b = 2E/m . Ne/ vo2
E/m = 1.5 x 1014 for a-particle (ES units)
For radium e, vo2 = 2.06 x 109 (should be vo !!!)
therefore b = (2 x 1.5 x 1014 x 200 x 4.65) / (1010 x 4.2 x 1018 )
= 6.6 x 10-12 cms
Since (...) radius of atom is of order 10-8 cm, it is seen that distance of approach to chargd centre is very small compared with radius of atom. In general it is obvious that the region where the deflecting force on the a-particles are large is very near centre of atom + (...) when field is due almost entirely to central charge.
Note, the symbol (...) denotes a part of the original text that is undecipherable.