The graph which depicts the results of Rutherford gold foil...

Rutherford carried out an experiment in which he bombarded a thin sheet of gold foil with $\alpha$-particles and then analysed the trajectory of these particles after they collided with the gold foil.

For a detector at a specific angle with respect to the incident beam, the number of particles per unit area striking the detector is given by the Rutherford formula,

$Y\left(\theta\right) = \dfrac{{N}_{i}nL{Z}^{2}{k}^{2}{e}^{4}}{4{r}^{2}{\left(KE\right)}^{2}\sin^{4}\left(\dfrac{\theta}{2}\right)}$

Here, ${N}_{i} =$ Number of incident alpha particles,

$n =$ Atoms per unit volume in target,

$L =$ Thickness of target,

$Z =$ Atomic number of target,

$e =$ Electron charge,

$k =$ Coulomb's constant,

$r =$ Distance between target and detector,

$KE =$ Kinetic energy of alpha particles,

$\theta =$ Scattering angle.

Therefore, $Y ∝ \dfrac{1}{\sin^{4}\left(\dfrac{\theta}{2}\right)}$