Input information
![Rutherford scattering | target atomic number | plutonium (chemical element) (atomic number): 94 kinetic energy | 8 MeV (megaelectronvolts) scattering angle | 60° (degrees) impact charge | 2 e (elementary charges)](../image_source/0cec46da470aef391699a3465b58a42b.png)
Rutherford scattering | target atomic number | plutonium (chemical element) (atomic number): 94 kinetic energy | 8 MeV (megaelectronvolts) scattering angle | 60° (degrees) impact charge | 2 e (elementary charges)
Result
![differential cross section | 1.145×10^-27 m^2/sr (square meters per steradian) = 11.45 b/sr (barns per steradian)](../image_source/a30e540d9429107184a9c46cce5cf45d.png)
differential cross section | 1.145×10^-27 m^2/sr (square meters per steradian) = 11.45 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/69d1063b6bf61a362ec15c52ee0ce800.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/2dfb570d64ad62de820ee0325e8504ac.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/7ecdf502f67a87ae57e08cb99602f7ea.png)
Schematic