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(C) According to the Rutherford scattering formula,the number of scattered $\alpha$-particles $N(	heta)$ detected at a scattering angle $	heta$ is g

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(C) According to the Rutherford scattering formula,the number of scattered $\alpha$-particles $N(	heta)$ detected at a scattering angle $	heta$ is given by:$N(	heta) \propto \frac{1}{\sin^4(	heta/2)}$As the scattering angle $	heta$ increases from $0$ to $\pi$,the value of $\sin(	heta/2)$ increases from $0$ to $1$.Consequently,the term $\sin^4(	heta/2)$ increases from $0$ to $1$.Therefore,the number of scattered particles $Y$ decreases very rapidly as $	heta$ increases.This relationship is best represented by a graph where $Y$ is very large at small angles and drops sharply as $	heta$ increases,which corresponds to the curve shown in option $C$.

The graph which depicts the results of the Rutherford gold foil experiment with $\alpha$-particles is:
$\theta$: Scattering angle
$Y$: Number of scattered $\alpha$-particles detected
(Plots are schematic and not to scale)

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The graph which depicts the results of the Rutherford gold foil experiment with $\alpha$-particles is:$\theta$: Scattering angle$Y$: Number of scattered $\alpha$-particles detected(Plots are schematic and not to scale)