Final answer:
The student's question is about the ratio of particles scattered at different angles from a thin gold foil, a key aspect of Rutherford's scattering experiment. An exact answer would require the use of the differential cross-section formula to integrate over the specified angular ranges. However, the provided reference text does not include sufficient details to perform this calculation.
Step-by-step explanation:
The question pertains to the scattering of 1 MeV particles from a thin gold foil, which is a reference to the famous Rutherford scattering experiment. In this experiment, most alpha particles passed through the gold foil, but a small fraction were deflected, and even fewer were deflected at large angles. This deflection occurs due to the Coulomb interaction between the positively charged alpha particles and the positively charged gold nuclei.
The ratio of the number of particles scattered at angles greater than 2° to those scattered at angles greater than 8° would depend on the details of the scattering process, more specifically on the differential cross-section of the scattering. In general, the number of particles scattered at larger angles is smaller because it requires closer encounters with the gold nucleus, which is less probable. The exact calculation of this ratio would involve integrating the differential cross-section over the angular ranges in question. However, for such specific values of angles, the angle differential cross-section formula derived from Rutherford's scattering experiment would need to be used.
The answer to this question is not provided in the reference text and would require additional information or calculations involving the scattering cross-section formula.