The theory of Rutherford scattering and its results


In this article, we are going to discuss The theory of Rutherford scattering and its Results. We are also going to discuss the theory and history of Rutherford scattering.

Coulomb scattering of the charged particle or  Rutherford scattering

The concept of the atom for the structure of the matter is one of the most important discoveries of the nineteenth century. But the most of the knowledge about the structure of an atom was obtained in the twentieth century. J.J Thomson proposed a model for an atom. According to J.J Thomson model, an atom is a positively charged sphere of radius about 1Aº. In this sphere mass and positive charge of the atom are equally distributed. An equal number of opposite i.e. negative charge is also embedded in it.

The theory of Rutherford scattering and its Results

Rutherford in 1906 started an important experiment of scattering of α-particles by the atom. In Rutherford scattering, he bombarded high energy α-particles on a thin foil. He found that α-particles have deviated from their paths. The deviation of α-particle from its path by the atom is called scattering. If we assume that the Thomson model is reliable with this model. Then the α-particle should be scattered within a scattering angle less than 1º. But his experiment shows that some of the particles were deflected through more than 90º. On their passage through a foil.

History of the Rutherford model

Geiger and Marsden in 1909, repeated this experiment. They used a high-density material such as gold. They found that most of the α-particles move through the gold foil without any deviation. While some of the particles are scattered by a small scattering angle.  And some of the particles are scattered by a large scattering angle. Even a very few particles experience backward scattering. This backward scattering and large angle scattering can be explained by Thomson atomic model.

The theory of Rutherford scattering and its Results
Rutherford atomic model

Rutherford proposed a new model for the atoms by which nucleus could be discovered in the atom. This new model of Rutherford was able to explain the reason behind large scattering. According to Rutherford, large angle scattering is possible only and only if all the positive charge of the atom is centered at the center. the α-particle is are scattered by the repulsive Coulomb interaction of positive charge of the atom.

According to the Rutherford atomic model, the entire positive charge and mass of the atom are concentrated in a very small volume as its center. The central core of the atom is now called the nucleus. The nucleus is surrounded by the cloud of electrons which makes the entire at atom neutral.

Results of Rutherford scattering formula
  1. The entire positive charge and the mass of the atom are concentrated at the center. This central core is called the nucleus.
  2. The mass of α-particle is assumed to be very low in comparison to the mass of Nucleus. So that the impact of α-particle on the atom does not change its position.
  3. Scattering of α-particle is only due to the repulsive Coulomb interaction. Between the α-particle and the atom.
  4. Scattering of α-particles does not affect the electrons around Nucleus.
  5. The nucleus in α-particle is assumed as point charges. And scattering is due to the repulsion force acting between α-particle and Nucleus.

Let the atomic number of the scattered atoms is Z. So the charge of Nucleus is +Ze and the charge of the α-particle is +2e. Thus the repulsive Coulombs force acting on Nucleus and the alpha particle is

F=K(ze)2e/r²            (1)

where K is constant. And r is the distance between the colliding particle and the scatterer. Due to the inverse square law of force, the trajectory of the alpha particle will be hyperbola whose focus is the nucleus of the atom.

The hyperbolic trajectory of α-particle
The conclusion of The theory of Rutherford scattering and its Results

In this particular article, The theory of Rutherford scattering and its Results, The concept of Rutherford scattering and its results is clear in the easiest way possible.







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