Rutherford's experiment

RUTHERFORD'S EXPERIMENT

- Computer programm - experiment simulation
    In the year 1898 Thomson created the idea of atom as the positive charged ball in which there are negative charges placed - the "plum cake" model. So summing up the whole atom were to be neutral.
    In the years 1909-1911 Ernest Ruthefordand his students - Hans Geiger (1882-1945) and Ernest Marsden conducted some experiments to search the problem of alpha particles scattering by the thin gold-leaf. Rutheford knew that the particles contain the 2e charge. The experiment caused the creation of the new model of atom - the "planetary" model.
    Rutheford suggested to hit the gold-leaf (picture no. 1) with fast alpha particles from the source ²¹⁴Po. (The source R was in the lead lining F). The particles felt from the source on the gold-leaf E and were observed by the microscope M. The whole experiment was in the metal lining A and was covered with the glass plate P. The instrument was attached to the footing B. The gold leaf was about 5*10^-7 meter thick. The scientist knew that reckoning the scattering angle could say much about the structure of atoms of the gold-leaf.
The alpha particles propagated on the atomic nucleuses

The alpha particles propagated on the atomic nucleuses

Rutheford made a theoretical analysis of angles of scattering in accordance with Thomson's theory of atom and in accordance with his own theory. He assumed that atom consisted of positive charged nucleus and negative charged electrons circling around the nucleus. Then his theoretic calculations he compared with the experiment result. Alpha particles going through atom created in accordance with the "plum cake" model wouldn't be strong abberated because the electric field in that atom wouldn't be strong. In the model created by Rutheford the field is much stronger near to the nucleus, so some of alpha particles are much more abberated. The other going in the far distance to the nucleus are almost not at all abberated. The probability that any alpha particle will hit the nucleus is small but there is such a chance.
Marsden-Geiger experiment

The models of the Thomson's atom and Rutheford's atom.

The experiment showed that there are some not much abberated alpha particles but also some abberated of a very big angle (135-150 degree). That occurrence couldn't be explained by some small, added aberrations. Experimental data proved the "planetary" model of atom.
Between an alpha particle and an atomic nucleus there subsist an interaction - the repulsing - according to Coulomb force:

F = (1/(4*pi*y0))*((2*Z*e^2)/(r^2))

(1)
where (2*e)- alpha particle charged, (Ze)- atomic nucleus charged, y₀ - permittivity of free space, r - distance between the nucleus and the particle. Then, according to the formula created by Rutherford> (we decided not to present the run of this thoughts leading to the formula because it's very complicated from the mathematical side), dN - the number of alpha particles scattered in a time unit inside the solid angle dQ is equal:

dN/dQ = n*(((2*e)*(Z*e))/(4*pi*y*4*E))*1/(sin^4 (G/2))

dN/dQ = n*(((2*e)*(Z*e))/(4*pi*y*4*E))*1/(sin^4 (G/2))

(2)
where n - alpha particle flux density, G - angle of scattering alpha (picture no. 2), E particles' energy.
On the base of the number of alpha particles scattered by the G angle the Z number of elementary, positive charges in the nucleus can be calculated. He found that the number is equal to the atomic number. If we know the charge of the nucleus we can calculate the upper limit of its radius (by the assumption that the nucleus is a ball). The of the alpha particles and the nucleus radius is smaller than the minimum limit r₀ between their centres in the moment of collision. To evaluate r₀ lets consider the central collision - scattering by the angle G = 180 degree. By the law of conservation of energy - in the moment, when the distance between the alpha particles and the nucleus is minimal, the kinetic energy of that alpha particle is completely changed to the energy of the interaction:

(m*v^2)/2 = ((2*e)*(Z*e))/(4*pi()*y0*r0)

(m*v^2)/2 = ((2*e)*(Z*e))/(4*pi()*y0*r0)

(3)
where m - alpha particle mass, v - alpha particle velocity before the collision.
After transformation:

r0 = ((2*e)*(Z*e))/2*pi()*y0*m*v^2)

(4)

The diagram showing the methode of the maximal radius of the atomic nucleus determination.

From the equation (4) for the gold of this experiment the r₀ value was about 3,1*10^-14 meter (the velocity of alpha particles was equal 1,9*10⁷ meter per second). Nucleus dimension have to be smaller than that quantity.
Summarising the results of his work Rutherford came to the opinion that atom consisted of a nucleus (of size 10^-15 to 10^-14 meter). The nucleus contains the whole positive charge and almost the whole atom's mass. Around the nucleus, on the area of the size of the order of 10^-10 meter, light electrons are circling. Electrons have to circle around the nucleus on orbits, not to fell down on the nucleus. The orbits depend on electrons energy. In atoms of the same element, electrons circle on the same characteristic, for that element, orbits - the optical spectrum of atoms of the same element is the same.
The Rutherford's atomic model

The model created by Rutherford had still some serious discordance. According to the classic science, electron moving around the nucleus should emit an electromagnetic wave. That kind of emission is connected with the escape of some energy from the electron-ion circuit. Electron should than move not by the circle but helical and finally collide with the nucleus. But atom is stable. Other discordance regarded the radiation - it were to be constant (because the time of electron's cycle in accordance with the lost of energy should change constantly) and spectral lines shouldn't occur.
In the planetary model of atom, the electron should emit energy and spirally fall on the nucleus.

In the planetary model of atom, the electron should emit energy and spirally fall on the nucleus.