Rutherford Scattering: Finding Cross Section & Solid Angle

[lippyka]

Hi I am revising for an exam and am a bit confused with Rutherford Scattering
- Finding the cross section (is the cross section different to the differential cross section?)
- Finding the solid angle.

So here is a past question: A beam of 6MeV alpha particles is incident on a platinum foil. A detector of entrance area 2cm^2 is positioned 30cm from the foil to collect alpha particles that have been scattered through 50°.

a) determine the distance of closest approach considering the conservation of KE to electric PE.

This i think i need to use the equation : D= zZ e^2 /4 pi ε0 × KE

b) Determine the solid angle of the detector

Here i am not sure whether i can use cross section = pi × b^2 , where b= impact parameter

c) determine the cross section for alpha particles to scatter into the detector.could somebody please help me with part b and c, and let me know whether I am correct with part a.
Many thanks in advance

 

[mfb]

I moved your thread to our homework section.

"The cross section" typically means the total cross section, which is the integral of the differential cross section over the whole solid angle (or whatever variable the "differential" has).

This i think i need to use the equation : D= zZ e^2 /4 pi ε0 × KE

Apart from missing brackets, that is the closest possible distance the particles can have, but I think the question asks about the closest approach for the given scattering angle, which is different.

Here i am not sure whether i can use cross section = pi × b^2 , where b= impact parameter

The solid angle of the detector is a purely geometric thing, it has nothing to do with the impacting beam.