In the Rutherford's nuclear model of the atom,the nucleus (radius about $10^{-15} \; m$) is analogous to the sun about which the electron moves in an orbit (radius $\approx 10^{-10} \; m$) like the earth orbits around the sun. If the dimensions of the solar system had the same proportions as those of the atom,would the earth be closer to or farther away from the sun than it actually is? The radius of the earth's orbit is about $1.5 \times 10^{11} \; m$. The radius of the sun is taken as $7 \times 10^{8} \; m$.

In Rutherford's experiment,the number of particles scattered at a $90^{\circ}$ angle is $x$ per second. The number of particles scattered per second at an angle of $60^{\circ}$ is:

$A$ $7.9 \text{ MeV}$ $\alpha$-particle scatters from a target material of atomic number $Z = 79$. From the given data,the estimated diameter of the nucleus of the target material is (approximately) . . . . . . $\text{m}$.
$\left[\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \text{ Nm}^2/\text{C}^2\right.$ and electron charge $\left.e = 1.6 \times 10^{-19} \text{ C}\right]$

Choose the correct alternative from the clues given at the end of each statement:
$(a)$ The size of the atom in Thomson's model is .......... the atomic size in Rutherford's model. (much greater than/no different from/much less than.)
$(b)$ In the ground state of .......... electrons are in stable equilibrium,while in .......... electrons always experience a net force. (Thomson's model/Rutherford's model.)
$(c)$ $A$ classical atom based on .......... is doomed to collapse. (Thomson's model/Rutherford's model.)
$(d)$ An atom has a nearly continuous mass distribution in a .......... but has a highly non-uniform mass distribution in .......... (Thomson's model/Rutherford's model.)
$(e)$ The positively charged part of the atom possesses most of the mass in .......... (Rutherford's model/both the models.)

In the Geiger-Marsden scattering experiment,the thickness of the thin gold foil is . . . . . . m.

Rutherford's $\alpha$-particle experiment showed that the atoms have