Read the following statements regarding the Geiger-Marsden ( α...

Statement (A) is incorrect. The fraction of $\alpha$-particles scattered at large angles is very small because the nucleus occupies an extremely small volume (small cross-sectional area) compared to the total volume of the atom, not simply because it is massive.

Statement (B) is correct. The distance of closest approach for a head-on collision is $r_0 = \dfrac{1}{4\pi\epsilon_0} \dfrac{2Ze^2}{K}$. Since $r_0 \propto \dfrac{1}{K}$, doubling the kinetic energy $K$ will exactly halve the distance of closest approach.

Statement (C) is correct. In Rutherford scattering, the collision between the $\alpha$-particle and the nucleus is considered elastic, meaning the total kinetic energy of the system is conserved.

Statement (D) is incorrect. The number of scattered particles is given by $N(\theta) \propto \dfrac{1}{\sin^4(\theta/2)}$. The minimum number of scattered particles occurs when the denominator is maximum, which happens at $\theta = 180^\circ$, not $90^\circ$.

Therefore, exactly 2 statements are correct.

Answer: 2