- #1
SredniVashtar
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In "Concepts of Modern Physics", 4th ed., Arthur Beiser obtains the following Rutherford formula
<br /> N[\theta ] = <br /> \frac<br /> {<br /> \left( \frac{q^2}{8 \pi \epsilon_0} \right)^2 <br /> \left( n d Z^2 \right) <br /> N_0<br /> }<br /> {<br /> T^2 \left( r^2 \sin ^4 \left( \frac{\theta}{2} \right) \right)<br /> }<br />
relating the number of alpha particles detected per unit area to the angle of scattering \theta. 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 N_0 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 \theta is inversely proportional to the fourth power of the sin of \frac{\theta}{2}.
My problem is that I don't understand why N\left(\theta\right) diverges when \theta goes to 0. Shouldn't I get a finite number, smaller than N_0, of particles per unit area ?
What am I missing?
<br /> N[\theta ] = <br /> \frac<br /> {<br /> \left( \frac{q^2}{8 \pi \epsilon_0} \right)^2 <br /> \left( n d Z^2 \right) <br /> N_0<br /> }<br /> {<br /> T^2 \left( r^2 \sin ^4 \left( \frac{\theta}{2} \right) \right)<br /> }<br />
relating the number of alpha particles detected per unit area to the angle of scattering \theta. 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 N_0 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 \theta is inversely proportional to the fourth power of the sin of \frac{\theta}{2}.
My problem is that I don't understand why N\left(\theta\right) diverges when \theta goes to 0. Shouldn't I get a finite number, smaller than N_0, of particles per unit area ?
What am I missing?