If in Rutherford's experiment,the number of particles scattered at $90^o$ angle are $28$ per min,then the number of scattered particles at an angle $60^o$ and $120^o$ will be:

The size of an atom is of the order of

$A$ $7.9 \text{ MeV}$ $\alpha$-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 $\left.e = 1.6 \times 10^{-19} \text{ C}\right]$

Given below are two statements:
$Statement$ $I$: Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it,is Rutherford's model.
$Statement$ $II$: An atom is a spherical cloud of positive charges with electrons embedded in it,is a special case of Rutherford's model.
In the light of the above statements,choose the most appropriate from the options given below.

The diagram shows the path of four $\alpha$-particles of the same energy being scattered by the nucleus of an atom. Which of these is/are not physically possible?

An $\alpha$-particle of energy $5 \text{ MeV}$ is moving forward for a head-on collision. The distance of closest approach from the nucleus of atomic number $Z=50$ is . . . . . . $\times 10^{-14} \text{ m}$.
$(k=9 \times 10^{9} \text{ SI}, e=1.6 \times 10^{-19} \text{ C}, 1 \text{ eV}=1.6 \times 10^{-19} \text{ J})$