# Rutherford Formula

1. Jun 28, 2010

### SredniVashtar

In "Concepts of Modern Physics", 4th ed., Arthur Beiser obtains the following Rutherford formula

$$N[\theta ] = \frac { \left( \frac{q^2}{8 \pi \epsilon_0} \right)^2 \left( n d Z^2 \right) N_0 } { T^2 \left( r^2 \sin ^4 \left( \frac{\theta}{2} \right) \right) }$$

relating the number of alpha particles detected per unit area to the angle of scattering $$\theta$$. 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?

2. Jun 28, 2010

### SredniVashtar

Ok, I guess I was missing the shape of the area associated with the angle $$\theta$$.