In the Geiger-Marsden experiment, the gold foil had a thickness of \(2.1\times10^{-7}\ \mathrm{m}\). Taking the radius of a gold atom as \(1.4\times10^{-10}\ \mathrm{m}\), the foil was about how many atoms thick?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 750
Think of the foil as layers of gold atoms packed one on top of another. Each layer is as thick as one atom, that is, one atomic diameter. The diameter is twice the radius.
\( \begin{aligned} D &= 2r \\ &= 2\times1.4\times10^{-10} \\ &= 2.8\times10^{-10}\ \mathrm{m} \end{aligned} \)
\( \begin{aligned} N &= \frac{2.1\times10^{-7}}{2.8\times10^{-10}} \\ &= 750 \end{aligned} \)
From the above, an α-particle crosses about 750 layers of atoms on its way through the foil. Even so, most α-particles go straight through, because an atom is mostly empty space.