Input information
![Rutherford scattering | target atomic number | radium (chemical element) (atomic number): 88 kinetic energy | 8 MeV (megaelectronvolts) scattering angle | 60° (degrees) impact charge | 2 e (elementary charges)](../image_source/e7536e9708e37089c2c441b4ed82cc32.png)
Rutherford scattering | target atomic number | radium (chemical element) (atomic number): 88 kinetic energy | 8 MeV (megaelectronvolts) scattering angle | 60° (degrees) impact charge | 2 e (elementary charges)
Result
![differential cross section | 1.004×10^-27 m^2/sr (square meters per steradian) = 10.04 b/sr (barns per steradian)](../image_source/f965e9c3f3df533c7bdd71aebbab4a0f.png)
differential cross section | 1.004×10^-27 m^2/sr (square meters per steradian) = 10.04 b/sr (barns per steradian)
Equation
![dσ/dΩ = ((q Z e)/(16 π ε_0 E_k))^2 csc^4(θ/2) | | dσ/dΩ | differential cross section Z | target atomic number E_k | kinetic energy θ | scattering angle q | impact charge e | elementary charge (≈ 1.602×10^-19 C) ε_0 | electric constant (≈ 8.85418781×10^-12 F/m)](../image_source/d46c1ca2f3be9b9cec042b364d036619.png)
dσ/dΩ = ((q Z e)/(16 π ε_0 E_k))^2 csc^4(θ/2) | | dσ/dΩ | differential cross section Z | target atomic number E_k | kinetic energy θ | scattering angle q | impact charge e | elementary charge (≈ 1.602×10^-19 C) ε_0 | electric constant (≈ 8.85418781×10^-12 F/m)
Impact parameter equations
![b = (e q Z sqrt((1 + cos(θ))/(1 - cos(θ))))/(8 ε_0 π E_k) | r_min = (b cos(θ/2))/(1 - sin(θ/2)) | q | impact charge Z | target atomic number E_k | kinetic energy θ | scattering angle b | impact parameter dσ/dΩ | differential cross section r_min | closest approach ε_0 | electric constant (≈ 8.85418781×10^-12 F/m) e | elementary charge (≈ 1.602×10^-19 C)](../image_source/582c82305335c7e15f01bfa4a9292af0.png)
b = (e q Z sqrt((1 + cos(θ))/(1 - cos(θ))))/(8 ε_0 π E_k) | r_min = (b cos(θ/2))/(1 - sin(θ/2)) | q | impact charge Z | target atomic number E_k | kinetic energy θ | scattering angle b | impact parameter dσ/dΩ | differential cross section r_min | closest approach ε_0 | electric constant (≈ 8.85418781×10^-12 F/m) e | elementary charge (≈ 1.602×10^-19 C)
Units
Schematic
![Schematic](../image_source/bbb9b910fefab4f3fed4f4e593ef631a.png)
Schematic