(a) Describe Rutherford's experiment and how it led to the structure of the
atom. How was he able to estimate the number of protons in a nucleus from the
scattering of the \(\alpha\) particles? (b) Consider the \({ }^{23} \mathrm{Na}\)
atom. Given that the radius and mass of the nucleus are \(3.04 \times 10^{-15}
\mathrm{~m}\) and \(3.82 \times 10^{-23} \mathrm{~g},\) respectively, calculate
the density of the nucleus in \(\mathrm{g} / \mathrm{cm}^{3}\). The radius of a
\({ }^{23}\) Na atom is \(186 \mathrm{pm}\). Calculate the density of the space
occupied by the electrons in the sodium atom. Do your results support
Rutherford's model of an atom? [The volume of a sphere is \((4 / 3) \pi r^{3},\)
where \(r\) is the radius. \(]\)