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Rutherford Scattering Scattering Cross-Section

Rutherford scattering is the elastic scattering of charged particles by the Coulomb interaction.

The scattering cross-section is proportional to the impact charge squared, the target atomic number squared, the sum of 1 and the cosine of the scattering angle divided by the difference between 1 and the cosine of the scattering angle, and the reciprocal of the kinetic energy squared.

Formula

{QuantityVariable["σ", "CrossSectionalArea"] == ((1 + Cos[QuantityVariable["θ", "Angle"]])*Quantity[1/(64*Pi), "ElementaryCharge"^2/"ElectricConstant"^2]*QuantityVariable["q", "ElectricCharge"]^2*QuantityVariable["Z", "Unitless"]^2)/((1 - Cos[QuantityVariable["θ", "Angle"]])*QuantityVariable[Subscript["E", "k"], "Energy"]^2), QuantityVariable["P(θ)", "Unitless"] == (Quantity[6.02214128999999968641024`7.047357180783782*^23, "Moles"^(-1)]*QuantityVariable["d", "MassDensity"]*QuantityVariable["t", "Thickness"]*QuantityVariable["σ", "CrossSectionalArea"])/QuantityVariable["M", "MolarMass"]}

symbol description physical quantity
σ scattering cross-section "CrossSectionalArea"
θ scattering angle "Angle"
q impact charge "ElectricCharge"
Z target atomic number "Unitless"
Ek kinetic energy "Energy"
P(θ) probability of scattering greater than θ "Unitless"
d density "MassDensity"
M molar mass "MolarMass"
t foil thickness "Thickness"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Rutherford Scattering Scattering Cross-Section"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject["Rutherford Scattering Scattering Cross-Section"]]
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Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Rutherford Scattering Scattering Cross-Section"], {QuantityVariable[ \!\(\*SubscriptBox[\("E"\), \("k"\)]\),"Energy"] -> Quantity[8, "Megaelectronvolts"], QuantityVariable["d","MassDensity"] -> Quantity[19.3`, ("Grams")/("Centimeters")^3], QuantityVariable["P(\[Theta])","Unitless"] -> None, QuantityVariable["\[Sigma]","CrossSectionalArea"] -> Quantity[1475.444827016474`, "Barns"], QuantityVariable["t","Thickness"] -> Quantity[1.`*^-6, "Meters"], QuantityVariable["Z","Unitless"] -> 79, QuantityVariable["\[Theta]","Angle"] -> Quantity[60, "AngularDegrees"]}]
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Source Metadata

  • Creator:
  • Date: 1911

Publisher Information