Question

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.

Answer 1

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.

Step-by-step 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) =
`(Ni*nt)/(16) * ((e^(2) )/(4*pi*e0))^(2) * (Z^(2)_(1) * Z^(2)_(2) )/(r^(2)*K^(2) *sin^(4) (tet/2) )`

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

`(N(50))/(N(6)) = (sin^(4) (3) )/(sin^(4) (25) ) \\(N(50))/(N(6)) = 2.35 * 10^(-4)`

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

`N(6) = (N(50))/(2.35*10^(-4) ) \\N(6) = (1 particles/seconds)/(2.35*10^(-4) ) \\N(6) = 4252 particles/seconds`

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.