First, check the choices, you don't have do accurate numerical calculation here. So, try to approximate and simplify your calculation.
Now, if you don't remember how cross section works. Just recognize that, the thicker scatterer, the less protons pass the way through it. You should also expect exponential behavior here (read about this topic if you don't notice that). You should also know that higher density of nuclei causes more scattering in the scatterer, so it decreases the number of protons passing the way through it. Combining this knowledge together and dimensional analysis. You have
, where
is the ratio of number of protons passing through the scatterer per number of incoming protons,
is the number density of nucleis in the scatterer,
is the cross-section area, and
is thickness.
Now, one proton per incident million is scattered. so,
Also, we can approximate
since the cross-section is very small (you can see from choices).
Therefore,
and
The correct answer is (C). 38 of 100 people answer it correctly.
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