Rutherford’s Model Of An Atoms

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Rutherford’s model of an atom which is also known as ” Alpha Particle Scattering Experiment “.This experiment was performed by two students of Rutherford’s  “H.Geiger  and  E. Marsden” in 1911. This experiment was performed  on the scattering of alpha-particle from thin foils and obtained an important insight into the structure of  an atom.An alpha-particle is a helium ion , i.e. a helium atom  from which both the electron have been removed. It has charge equal to +2e and its mass is nearly four time the mass of  a proton.

The experiment tested the validity of the Thomson atomic model, which postulated that the positive charges and negative electrons were uniformly distributed over the spherical atomic volume, the radius of which was of the order of a few angstrom.

The Experimental  Arrangement Of Geiger-Marsden :-

They placed a radioactive source of alpha-particles like bismuth which is enclosed by in thick lead block, provided with narrow opening. From  this the source of alpha-particles are collimated into a narrow beam which is allowed to fall on a thin gold foil of thickness 2×10^-7 m.
The scattered alpha-particle in different directions are observed with the help of rotable detector which consist of a zinc sulphate screen and a microscope. Whenever an alpha-particle strikes the zinc sulphate screen, it produces  a tiny flash, which is viewed through the microscope. Through this way the number of alpha-particles  scattered at different angles were counted.

The theoretical calculations predict that the probability for an alpha-particle to be scattered on such an atom with a scattering angle exceeding 90° is of the order of 10^-3500, while Gieger-Marsden showed that approximately 1 in 10,000 alpha-particle was scattered with a scattering angle greater than 90°(probability 10,000).

Rutherford’s Observation:-

Most of the alpha-particle passes straight through gold foil or suffer only small deflection.
A few alpha-particle, 1 in 8000 get deflected by 90°or more.
An alpha-particle gets rebounded from gold foil, without suffering a deflection of nearly 180°. 

Rutherford’s Conclusion:-

As most of the alpha-particle passes straight through the foil, so most of the space within the atom is empty.
To explain large angle scattering  , Rutherford’s suggested that  all the positive charges and the mass of the atom is concentrated in a very small called the nucleus of the atom.

The nucleus is surrounded by a cloud of electrons whose total negative charge is equal to the total positive charge on the nucleus so  that the atom as a whole is electrically neutral.

In alpha-particle scattering the positively charged alpha-particle has a repulsive  Coulomb interaction with the more massive and positively charged nucleus. The interaction produces a hyperbolic trajectory of the alpha-particle, and the scattering angle is a function of the impact parameter b. The limiting case is a direct hit with   b = 0  and  angle = π  (backscattering)  that, assuming conservation of the energy , determines the distance of the closest approach D in the backscattering interaction.

The repulsive  Coulomb force between the alpha-particle (charge  +2e) and the nucleus (charge  +Ze) is governed by 1/r^2  as follows:-

Coulomb force = 2Ze^2/4π€r^2

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