Rutherford’s Experiment: Hyperbola

Question

In May 1911, Ernest Rutherford published a paper in Philosophical Magazine. In this article, he described the motion of alpha particles as they are shot at a piece of gold foil 0.00004 cm thick. The figure shows a diagram from the scientist’s paper that indicates that the deflected alpha particles follow the path of one branch of a hyperbola and the asymptotes are at an angle of 45 degrees from the orgin. (a) Find an equation of the asymptotes under this scenario. a b b y ?? .  y ? and  x a (b) If the vertex of the path of the alpha particles is 3 cm from the center of the hyperbola, find a model that describes the path of the particle.

Answer 1

Center of hyperbola = origin

 

Vertex of hyperbole = 3cm away from origin

 

That is a=3

 

Asymptote are at an angle of 45degrees

 

The equation of Asymptote ----

a/b. =+- tan (45)

So, Asymptote are.       

  a= b.    and

  a=-b

 

So, b=3

 

So, the equation of hyperbola.  is

      (x^2)/9.      -(y^2)/9   =1