In the Geiger-Marsden experiment, the number | vedclass

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(C) In the Geiger-Marsden experiment, the number of scattered $\alpha$-particles $N(	heta)$ at a scattering angle $	heta$ is given by the relation:

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(C) In the Geiger-Marsden experiment, the number of scattered $\alpha$-particles $N(	heta)$ at a scattering angle $	heta$ is given by the relation:
$N(	heta) \propto \frac{1}{\sin^4(	heta/2)}$
Taking the logarithm on both sides:
$\log N(	heta) \propto -4 \log(\sin(	heta/2))$
As the scattering angle $	heta$ increases, the value of $\sin(	heta/2)$ increases, which means $\sin^4(	heta/2)$ increases rapidly.
Consequently, the number of scattered particles $N(	heta)$ decreases very sharply as the scattering angle $	heta$ increases.
This relationship is represented by a downward-sloping curve on a semi-logarithmic plot, where the y-axis is logarithmic $(N(	heta))$ and the x-axis is linear $(	heta)$.
Among the given options, the plot in option $(3)$ correctly shows this sharp decrease in the number of scattered $\alpha$-particles as the scattering angle increases.

In the Geiger-Marsden experiment, the number of scattered $\alpha$-particles $N(\theta)$ is plotted as a function of the scattering angle $\theta$. Which of the following options represents the correct plot?

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