In the result of the Geiger-Marsden experiment, by which the trajectory of the $\alpha $ -particle can be calculated ?

If scattering particles are $56$ for ${90^o}$ angle then this will be at ${60^o}$ angle

Based on which experiment did the Rutherford nuclear model come from? 

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

Assertion $(A)$ : The magnetic moment $(\mu)$ of an electron revolving around the nucleus decreases with increasing principle quantum number $(n)$.

Reason $(R)$ : Magnetic moment of the revolving electron, $\mu \propto n$.

Consider the following statements:

$I$. All isotopes of an element have the same number of neutrons.

$II$. Only one isotope of an element can be stable and non-radioactive.

$III$. All elements have isotopes.

$IV$. All isotopes of carbon can form chemical compounds with oxygen-$16$.

Choose the correct option regarding an isotope.