Rutherford Scattering Experiment

Rutherford Scattering Experiment

The next step in the development of atomic model was given by Ernest Rutherford in 1911. Rutherford used a "Gold foil experiment" for explaining the atomic model given by J. J. Thomson. A decades earlier, Rutherford only identified one of type of radiation given off by radioactive elements like polonium, uranium etc and named them as alpha particles.

The alpha particles are fast moving and positively charged Helium nuclei with two protons and two neutrons.
Rutherford observed the deflection of alpha particles after passing through metal sheet and purposed his atomic model also called as planetary model because of its resembles with arrangement of plants around the sun.

Rutherford’s Alpha Scattering Experiment

Back to Top

Rutherford directed a narrow beam of alpha particles (after passing through a slit in a lead screen) obtained from polonium (²¹⁴Po) at an extremely thin sheet (about 5 $\times$10^-7 meter thick) of a metal like silver and gold.

After passing through the metal sheet, the alpha particles strike on fluorescent screen which was coated with zinc sulphide and produce a visible flash of light called scintillation.

Rutherford was expecting results according to the plum pudding model in which electrons and protons were distributed randomly. He was expecting that all alpha beams will move in the same direction of propagation with a little deflection. But results were much more different than his expectations.

Observation of Rutherford's alpha scattering experiment

Rutherford observed that most of alpha particles strike on the fluorescent screen without any deflection. However very few alpha particles deflected slightly and very less number of alpha particle; approx one particle deflect with the angle of 180°, i.e. almost bounce back.

Conclusion of Rutherford's Alpha Scattering Experiment

Based on the observation of alpha scattering experiment combined with the discovery of neutrons by James Chadwick, Rutherford concluded.

• An atom consists of a minute positively charged body at its center called as nucleus. The nucleus though small, contains all the protons and neutrons. Since the total mass of atom is because of protons and neutrons, hence the entire mass located at the center of atom. Hence few alpha particles deflected due to positive charge of nucleus.

• An atom consists of a sufficient number of extremely small negatively charged electrons distributed around the nucleus to balance the positive charge of nucleus. Hence maximum volume of an atom remains empty so many alpha particles moved without any deflection.

• Since very less number of alpha particles deflected, hence the volume of nucleus is very less compare to whole atom. The size of nucleus is less than 2x 10^-14 m while the size of an atom is around 10^-10 m.

Objection of Rutherford's Alpha Scattering Experiment

1. By following the classic electromagnetic science J.C.Maxwell had shown that whenever an electric charge emits radiation and loses energy when it is subjected to acceleration. In an atom, electron is also negatively charged particle; hence it must radiate energy during its movement around the nucleus and should lose energy and reached to zero. As a result, its orbit should become smaller and smaller and finally it should drop in to the nucleus in a helical path instead of circular path. In other words, an atom is not a stable species. On the contrary atom is stable and electrons and their energy in one of these orbits stay same.
2. Another discordance regarded the Rutherford's experiments was the spectrum obtained from the electron. An electron which continually emitted radiation must forms a continuous atomic spectrum. In other words there must be no line for fixed frequency. However the atomic spectrum is not continues spectrum but a line spectrum with many lines of fix frequency. Hence the Rutherford atomic model failed to explain the line spectrum of atoms. To overcome the first objection that why the electrons do not fall into the nucleus on account of mutual electrostatic attraction, Rutherford gave the explanation that the electrons are revolving with extremely high speed and at great distance from center. So centrifugal force arising from this motion balances the force of electrostatic attraction. Hence electrons do not fall in nucleus to form stable atom. But there was no clarification for atomic spectrum pattern.

Rutherford Scattering Formula

 

When an alpha particle strike to a positively charge body that is nucleus, the electrostatic force of repulsion worked strongly and alpha particles get scattered. The scattering process can be considered as cross section for interaction with nucleus which has point charge Z_e.

Let us take $\theta $ is the scattering angle and b is the impact parameter, the number of particles striking the per unit are of detector is given by Rutherford formula.

Rutherford Scattering Derivation

An alpha particle which scatters by the central positive charge of nucleus leads to a hyperbolic trajectory.
By using the scattering angle $\theta$, and momentum (p) of alpha particle, we can calculate the impact parameter (b) and the closest approach to the target nucleus.

According to Rutherford formula the number of alpha particle deflected by the angle $\theta$ is inversely proportional to the fourth power of the sine function of one half the angle of deflection