Which scientist gave plum pudding model of the atom ? 

Which of the following statements are true regarding Bohr's model of hydrogen atom

$(I)$ Orbiting speed of electron decreases as it shifts to discrete orbits away from the nucleus

$(II)$ Radii of allowed orbits of electron are proportional to the principal quantum number

$(III)$ Frequency with which electrons orbits around the nucleus in discrete orbits is inversely proportional to the principal quantum number

$(IV)$ Binding force with which the electron is bound to the nucleus increases as it shifts to outer orbitsSelect correct answer using the codes given belowCodes :

An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius $r$. The Coulomb force $\vec{F}$ between the two is

The graph which depicts the results of Rutherform gold foil experiment with $\alpha$ -particales is

$\theta:$ Scattering angle

$\mathrm{Y}:$ Number of scattered $\alpha$ -particles detected

(Plots are schematic and not to scale)

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.

An alpha nucleus of energy $\frac{1}{2}mv^2$ bombards a heavy nuclear target of charge $Ze.$ Then the distance of closest approach for the alpha nucleus will be proportional to