In Rutherford scattering the number of alpha particles detected per unit solid angle at scattering angle theta is proportional to 1/sin^4(theta/2) for a fixed beam, foil and detector distance. The ratio of the count at theta=60 deg to that at theta=120 deg is

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In Rutherford scattering the number of alpha particles detected per unit solid angle at scattering angle $θ$ is proportional to $1/ sin^{4} (θ /2)$ for a fixed beam, foil and detector distance. The ratio of the count at $θ = 6 0^{\circ}$ to that at $θ = 12 0^{\circ}$ is

N is proportional to

1/ sin^{4} (θ /2)

. N(60)/N(120) =

sin^{4} (6 0^{\circ}) / sin^{4} (3 0^{\circ})

= (0.5625)/(0.0625) = 9. Using

sin^{2}

instead of

sin^{4}

gives 3.