What is the Kinetic Energy of Alpha Particles Scattered by an Aluminum Plate?

[jinn]

Homework Statement

Onto an Aluminium 50μm thick plate, we send a beam of alpha particles with unknown kinetic energy. the cross section of the beam is 2cm², density 10¹³ / scm² . Whats the kinetic energy of the particles if every second we sense 10⁵ scattered particles between the angles 40° and 41°? Take into count only the Coulumb interaction and the density of Aluminium is 1850 kg/m³

Homework Equations

The Attempt at a Solution

 

[ProfuselyQuarky]

You have to show your attempt first! :)

 

[jinn]

first of all my understanding of scattering is shamefully low so please keep in mind...

σdif. = (z₁²*z₂²) / 16T_α² * 1/ sin⁴(ϑ/2)
dΩ= 2πsinϑdϑ
σ_R=∫σdif dϑ σdif = dσ/dΩ and the integral borders are 40° and 41°

now those 10⁵ = ndσ_r ? where d is the thickness and n = densiti times N_A/M

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