Input information
![Rutherford scattering | target atomic number | thallium (chemical element) (atomic number): 81 kinetic energy | 8 MeV (megaelectronvolts) scattering angle | 60° (degrees) impact charge | 2 e (elementary charges)](../image_source/9ba9a45baa6011af0124de43d3e77cb9.png)
Rutherford scattering | target atomic number | thallium (chemical element) (atomic number): 81 kinetic energy | 8 MeV (megaelectronvolts) scattering angle | 60° (degrees) impact charge | 2 e (elementary charges)
Result
![differential cross section | 8.503×10^-28 m^2/sr (square meters per steradian) = 8.503 b/sr (barns per steradian)](../image_source/9c3e2025cee8d5523b342870c200d559.png)
differential cross section | 8.503×10^-28 m^2/sr (square meters per steradian) = 8.503 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/19d8afaa26da854d8b41efd5a0b13001.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/82bd39192e48327a9ccf82805e85df36.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/c16c14b3052b7accfbac42aa7b10544e.png)
Schematic