Alpha Ray Scattering Experiment and Rutherford Model of Atom:
In 1911, scientist Rutherford and his two colleagues Geiger and Marsden, used an experiment to detect the structure of atom whose outline is shown in figure.
In this experiment a radioactive substance polonium (or Radon) placed in lead box A. The α-particle (which are actually the Helium atoms 2He4 nucleus) of high kinetic energy emanate from this box. After diaphragm D1 and D2, a-particles are collimated on a thin gold foil G in the form of a narrow beam. The thickness of gold foil is about 10-5 cm and due to its thin pin, α-particle deflects through a single collision. Gold foil is taken because (i) Gold foil can be made very thin, (ii) The gold nucleus is heavy for α-particle deflection.
Rutherford observed that α-particles passing through foil deflected in different directions. The occurrence of deflection from its path due to the collision of atoms of matter of alpha particles is called scattering. The scattered α-particles are focussed on a fluorescent screen S, from which each α-particle generates an fluorescence. Fluorescence generated in a certain direction can be counted by moving the microscope in any direction, meaning that the α-particle can be counted in that direction. A fluorescence counter also be used in the place of fluorescent screen and microscope. This complete management is kept in vaccum so that there is no collision of α-particle with any air particle.
(i) “The most of α-particles pass straight through the gold foil.” With this test, Rutherford concluded that most of the atom is hollow. It is clear the this is against the Thomson’s nuclear model. According to Thomson, atom is a solid ball of positive charge. If atom is a solid ball then how α-particles based through it.
(ii) “Some α-particles are deflected from their path with small angle.” The α-particle has positive charge so its scattering is possible only with some positive charge item. Thus Rutherford concluded that the total positive ions should be concentrated in one place. Through this test Thomson’s model was rejected, according to which the amount of positive charge is distributed evenly at the atom.
(iii) “Very small number of α-particles (one in 8000) display posterior scattering meaning deflected at 90° or more angle from their route or returning back.” From this test it was concluded that the concentration of all mass of the atom is at very area, which scattered nucleus. All mass of atom is also concentrated in the nucleus.
The size of the atom will be as small, the α-particles will reach the nucleus i.e., lesser the number of α-particles being scattered over angle 90°.
On calculation, the radius of nucleus is only 10000th in size of the atom. The remaining empty space of the atom contains only electrons.
Postulate of the nucleus is the most important fact of the structure of the atom and this gives a successful interpretation of Rutherford’s experimental result. Rutherford has interpretated his test as figure. It is clear from the figure that the α-particles that are far away from the nucleus, they cross right away without distracting foil. As the α-particle approaches the nucleus, the scattering begins. The scattering angle increases when they move towards nucleus.
(iv) Experiment of α-particles scattering proved the Coulomb’s law. Rutherford believed that the repulsive force that takes place between the positive α-particles and positive nucleus is given by Coulomb’s law.
That is, the repulsive force is inversely proportional to the square of distance from the nucleus of the particle. Due to this force the direction of α-particle becomes hyperbolic as shown in the figure. As the value of distance ‘r’ decreases, the value of F increases rapidly. Therefore, when passing through the atom, the repulsive force on which the particle stays away from the nucleus is less, so that it goes straight to initial path without being deflected, but as far as the alpha particle passes near the nucleus, the more repulsive force it feels, and the result is that it is scattering by the more angle (figure). The change of scattering angle θ with the distance r of the α-particle from the nucleus is shown in figure. In this experiment the change of the scattered angle can not be known for the distance of a particular α particle.
So, the graph can not be drawn in experimental form. Rutherford computed the number of α-particles scattered at various angles. Based on the Coulomb’s law and they found the number of particles (N) that are scattered at an angle (θ) is inversely proportional to sin4 (θ/ 2). i.e.,
The graph between N and θ is shown in figure. This relation proved to be true by the experiment of Geiger and Marsden in 1993. This concludes that the dispersion of α-particles by the nucleus is according to the Coulomb’s law which is also applicable to atomic distances (to 10-14 m).
(v) Rutherford extracted the number of α-particles scattered in a certain direction from foil of various metals (like-gold, silver and platinum etc.) by experiments and found that this number is different for different metal foil. Therefore they concluded that the amount of positive charge differ in the nuclei of different metals. The high positive charge in the nucleus, the α-particle will be repelled by the more force than that nucleus of less change.
Rutherford calculate the number of α-particles that are scattered at a certain angle and range is proportional to the square of positive charge in the metal and nucleus.
On this basis in 1920, the scientist Chadwick found that the quantity of positive charge in the metal nucleus is Ze, where Z is a constant for the metal. It is known as atomic number and e is a charge of electron.
Distance of closest approach (size of nucleus): The minimum distance from the nucleus up to which an energetic α-particle travelling directly towards the nucleus can move before coming to rest and retrace its own path is known as distance of closest approach. This distance is represented by r0.
Rutherford made the following assumptions for the calculation of distance:
(i) The atomic nucleus is so heavy that it’s motion during the impact is diregarded.
(ii) The nucleus and the alpha particle both are taken as point charges having no dimensions.
(iii) The scattering is due to elastic collosion between nucleus and α-particle.
Impact parameter: It is defined as the perpendicular distance of the initial velocity vector of the alpha particle from the central line of the nucleus, when the particle is far away from the nucleus of the atom. In fact, impact parameter determine the trajectory traced by an alpha particle in passing through the gold foil.
The impact parameter ‘b’ is calculated by the formula:
