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Rutherford's Notebook

Rutherford's Notebook

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.

plumpud copy.GIF (1154 bytes)

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.