Final answer:
In Rutherford's experiment, only a small percentage of alpha particles were scattered to large angles from the gold foil. To calculate the fraction of particles scattered through angles greater than 7°, we can use the Rutherford scattering formula and integrate it over the desired range.
Step-by-step explanation:
In Rutherford's experiment, the majority of alpha particles passed through the gold foil with minimal deflection.
However, a small percentage (about 1 in 8000 particles) were scattered to large angles, and some even bounced back towards the source.
To calculate the fraction of particles scattered through angles greater than 7°, we can use the Rutherford scattering formula:
dΩ = (Z^2 e^4 / 16πε0^2 E^2) [(1 + cos²θ) / (sin⁴(θ/2))]
Where dΩ is the solid angle, Z is the atomic number of the target material, e is the elementary charge, ε0 is the vacuum permittivity, E is the energy of the alpha particle, and θ is the scattering angle.
We can then integrate the Rutherford scattering formula from 7° to 180° and divide it by the total scattering cross-section to find the fraction of particles scattered through angles greater than 7°.