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Rutherford Formula

  1. Jun 28, 2010 #1
    In "Concepts of Modern Physics", 4th ed., Arthur Beiser obtains the following Rutherford formula

    N[\theta ] =
    \left( \frac{q^2}{8 \pi \epsilon_0} \right)^2
    \left( n d Z^2 \right)
    T^2 \left( r^2 \sin ^4 \left( \frac{\theta}{2} \right) \right)

    relating the number of alpha particles detected per unit area to the angle of scattering [tex]\theta[/tex]. Here, d is the thickness of the foil, n is the number of gold atoms per unit volume, T is the kinetic energy of the alpha particles, r is the distance target-screen and [tex]N_0[/tex] is the total number of alpha particles that strike the foil during the experiment.
    The number of particles per unit area around the direction at an angle [tex]\theta[/tex] is inversely proportional to the fourth power of the sin of [tex]\frac{\theta}{2}[/tex].

    My problem is that I don't understand why [tex]N\left(\theta\right)[/tex] diverges when [tex]\theta[/tex] goes to 0. Shouldn't I get a finite number, smaller than [tex]N_0[/tex], of particles per unit area ?
    What am I missing?
  2. jcsd
  3. Jun 28, 2010 #2
    Ok, I guess I was missing the shape of the area associated with the angle [tex]\theta[/tex].
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