I'm struggling to understand the importance of the differential cross-sectional area in Rutherford's scattering experiment, dσ/dθ. In one part of my course notes it is explained as 'the number of scatterings between θ and θ + dθ per unit flux, per unit range of angle'. However, dσ itself is described as the 'infinitesimal effective area for collision'. The graph of dσ/dθ shows a large reduction in the number of scatterings as the scattering angle is increased, but only for small angles. At larger θ, increasing θ has very little effect on the number of scatterings.(adsbygoogle = window.adsbygoogle || []).push({});

Am I understanding the results correctly? Is the 'effective area for collision' unaffected by change of scattering angle, only the number of scatterings is affected? If so, why is it called the 'differential cross-sectional area' when the number of observed scatterings is the only thing that changes, not the actual effective area for collision?

In my notes it is stated: 'Although the diﬀerential cross-section falls rapidly with the scattering angle, the cross-section at large angles is still much larger than would have been obtained from Thomson’s ‘current cake’ model of the atom in which electrons are embedded in a ‘dough’ of positive charge.'

Why is this?

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# I Differential cross-sectional area - Rutherford's experiment

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