Students want to construct a scattering experiment using a powerful source of 5.5-MeV alpha particles to scatter from a gold foil. They want to be able to count 1 particle/s at 50 degrees, but their detector is limited to a maximum count rate of 2000 particles/s. Their detector subtends a small angle. Will their experiment work without modifying the detector if the other angle they want to measure is 6 degrees? Explain.

we know our detector is limited to a maximum count rate of 2000 particles/s, and we would expect the count of 4252 particles/s as angle of 6 degree. That means we would have to modify our detector if we want to measure proper count number.

Explanation:

To get the number of particle  scattered per unit area, N(Ф) into the ring at the scattering angle Ф is

Ф = tet

N(tet) =

We can first calculate ratio of scattered particles at 50 and 6 degree angles using the equation

from there we can calculate number of scattered particles at 6 degree

we know our detector is limited to a maximum count rate of 2000 particles/s, and we would expect the count of 4252 particles/s as angle of 6 degree. That means we would have to modify our detector if we want to measure proper count number.

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explanation: