Wasn't Rutherford's assumption of gold foil to be made of single layer wrong?

Question

My teacher taught about Rutherford's gold foil experiment today. Sir said that, Rutherford used gold foil of thickness $10^{-7}$ m and concluded atom to be of size $10^{-10}$ m. Sir also said that Rutherford assumed foil to be consisting of only single layer of gold atoms.

What I thought was, if Rutherford used gold foil of $10^{-7}$ thickness, which is greater than the size of atom [$10^{-10}$] which he had concluded. So, gold foil should be made of more than single layer of atoms. But this would be against his assumption. If we assume gold foil to be consisting of more than one layer of gold atoms. Then we will be in need to know the structure of gold, i.e to know whether it has atoms in ABAB.. or AAAA.. or ABCABC... type of arrangement. My book says that gold has ABCABC... or ccp arrangement, it mean that there is no vertical allignment of atoms, thus there will be no vertical allignment of nuclei. It makes significant changes to Rutherford's predictions with respect to deviations. Won't it?

Answer 1

You were confused about the result of the experiment. It did not measure the size of the atom, but the size of the nuclei. Nucleus is the area of concentrated positive charge in the core of the atom, and is only a very small fraction the size of the atom itself.

And the result, $10^{-15}\ \mathrm{m}$, was the size of the nuclei, while the size of gold atoms has the order of magnitude of ångströms ($1\ \mathrm{\mathring{A}}=10^{-10}\ \mathrm{m}$).

The measurement comes from the analysis deflection angle of alpha particles when hitting the nuclei. The one-layer-of-atom assumption leaded to Rutherford to use a mathematical model for one single collision to analyze the angular distribution. Because the nucleus is so small, even if there were a small number of layers, most alpha particles will still only have one collision and the result will be correct.

However, the alpha particle was passing through some hundreds of atoms and many particles actually were deflected multiple times. The calculation would be much more complicated. Even if he knew the number of layers of atoms and tried to do it the right way, he might not be able to arrive at the correct number. Of course people back then would not be able to know that, but nevertheless, the existence of nucleus is still evident and Rutherford did almost get the order of magnitude right.