Atoms

In Thomson's model, the positive charge is spread throughout the atom, so the atom's size is of atomic order. Rutherford's model says most mass and positive charge are concentrated in a tiny nucleus, so the atom is much larger than the nucleus. Therefore, the size of the atom in Thomson's model is much greater than the atomic size in Rutherford's model.

In Thomson's model, the positive charge is uniformly distributed and the electrons are embedded in it, so electrons can be in stable equilibrium. In Rutherford's model, electrons revolve around the nucleus and are continuously acted on by the attractive force, so they always experience a net force. Hence the blanks are Thomson's model and Rutherford's model.

A classical atom based on Rutherford's model is doomed to collapse because the revolving electron should continuously radiate energy and spiral into the nucleus.

In Thomson's model, mass is nearly continuously distributed throughout the atom. In Rutherford's model, most of the mass is concentrated in the tiny nucleus, so the mass distribution is highly non-uniform. Therefore the blanks are Thomson's model and Rutherford's model.

In Rutherford's model, the positively charged nucleus possesses most of the mass of the atom. So the correct choice is Rutherford's model.

If a thin sheet of solid hydrogen is used instead of gold foil, the scattering would be much smaller. Hydrogen nuclei are very light and there is no large central charge like in gold to cause strong repulsion. So most $1particles would pass through with little or no deflection, and large-angle scattering or backscattering would be very rare. Compared with gold foil, the number of scintillations at large angles would be much less.

Use $h\nu = E$.

Given energy difference, $E = 2.3\,\text{eV}$.

Convert to joules:
$$E = 2.3 \times 1.6\times 10^{-19} = 3.68\times 10^{-19}\,\text{J}$$

Now,
$$\nu = \frac{E}{h} = \frac{3.68\times 10^{-19}}{6.6\times 10^{-34}}$$
$$\nu \approx 5.6\times 10^{14}\,\text{Hz}$$
So the frequency is about **$5.56\times 10^{14}\,\text{Hz}$**.