Rutherford's atomic model

The Rutherford model of the atom is a model of the atom or the internal structure of the atom proposed by the British-New Zealand chemist and physicist Ernest Rutherford. in 1911, to explain the results of his "gold foil experiment".

Rutherford concluded that the mass of the atom was concentrated in a small region of positive charges that impeded the passage of alpha particles. He later proposed a new atomic model that possessed a nucleus or center in which Thomson's Atomic Model could not explain how charge is held on the electrons within the atom. He, too, could not explain the stability of an atom. The theory did not mention anything about the nucleus of the atom.

The mass and positive charge are concentrated in it, and the negatively charged electrons are found in the extra-nuclear zone.

Model of a Rutherford atom. He proposed a core with protons (black in the center) and electrons (red) rotating around it.

History

Before Rutherford proposed his atomic model, physicists accepted that the electrical charges in the atom had a more or less uniform distribution. Rutherford tried to see what the scattering of alpha particles by atoms in very thin gold foil was like. The angles resulting from the deflection of the particles would supposedly provide information about how the charge distribution was in the atoms. It was to be expected that, if the charges were evenly distributed according to Thomson's atomic model, most of the particles would pass through the thin sheet with only slight deflections, following an approximately straight trajectory. Although this was true for most of the alpha particles, a significant number of these suffered deflections of close to 180º, that is, they practically bounced in the opposite direction to the incident.

Rutherford thought that not a sufficient fraction of particles bounced in the opposite direction could be explained by assuming the existence of strong concentrations of positive charge in the atom. Newtonian mechanics in conjunction with Coulomb's law predicts that the angle of deflection of a relatively light alpha particle by a heavier gold atom depends on the "impact parameter" or distance between the trajectory of the particle and the nucleus:

(1)χ χ =2π π − − 2#− − 1 (2K/(E0b)1+2K/(E0b)2){displaystyle chi =2pi -2cos ^{-1}left({frac {2K/(E_{0}b)}{sqrt {1+2K/(E_{0}b)^{2}}}}}}{right)}

Where:

K=(qN/4π π ε ε 0){displaystyle K=(q_{N}/4pi varepsilon _{0}),}, being ε ε 0{displaystyle varepsilon} the dielectric constant of void and qN{displaystyle q_{N},} the electric charge of the dispersed center.

E0{displaystyle E_{0},}, is the initial kinetic energy of the alpha particle incident.

b{displaystyle b,} is the impact parameter.

Since Rutherford observed an appreciable fraction of "bounced" for which the angle of deflection is close to χ ≈ π, from the inverse relation a (1):

(2)b=2KE0cot χ χ 2{displaystyle b={frac {2K}{E_{0}}}}{cot {frac {chi}{2}}}}}}

it follows that the impact parameter must be rather less than the atomic radius. In fact, the impact parameter necessary to obtain an appreciable fraction of "bounced" It was used to make an estimate of the size of the atomic nucleus, which turns out to be about a hundred thousand times smaller than the atomic diameter. This fact turned out to be the uniformable capacity on the positive charge of neutrons.

The importance of the model and limitations

The importance of Rutherford's model resided in proposing for the first time the existence of a central nucleus in the atom (a term coined by Rutherford himself in 1912, a year after the results of Geiger and Mardsen were officially announced). What Rutherford considered essential, to explain the experimental results, was "a concentration of charge" in the center of the atom, since, without it, it could not be explained that some particles were rebounded in almost the opposite direction to the incident one. This was a crucial step in the understanding of matter, since it implied the existence of an atomic nucleus where all the positive charge and more than 99.9% of the mass were concentrated. Estimates of the nucleus revealed that the atom was mostly empty.

Rutherford proposed that the electrons would orbit in that empty space around a tiny atomic nucleus, located in the center of the atom. In addition, several new problems were opened that would lead to the discovery of new facts and theories when trying to explain them:

• On the one hand, the problem was raised as to how a set of positive loads could be joined in such a small volume, which subsequently led to the postulation and discovery of the strong nuclear force, which is one of the four fundamental interactions.
• On the other hand there was another difficulty coming from classical electrodynamics that predicts that a charged and accelerated particle, as would be the case of electrons orbiting around the nucleus, would produce electromagnetic radiation, losing energy and finally falling over the nucleus. Newton's laws, together with Maxwell's equations of electromagnetism applied to Rutherford's atom, lead to a time of order 10− − 10{displaystyle 10^{-10}s, all the energy of the atom would have been radiated, with the consequent fall of the electrons over the nucleus. It is therefore a physically unstable model, from the point of view of classical physics.

According to Rutherford, the orbits of the electrons are not very well defined and form a complex structure around the nucleus, giving it a somewhat indefinite size and shape. The results of his experiment allowed him to calculate that the atomic radius was ten thousand times greater than the nucleus itself, and consequently, that the interior of an atom is practically empty.

Later models

Rutherford's atomic model was soon replaced by the Bohr model. Bohr tried to explain phenomenologically that only some orbits of the electrons are possible. Which would account for the emission and absorption spectra of the atoms in the form of discrete bands.

The Bohr model formally «solved» the problem, coming from electrodynamics, postulating that electrons simply did not radiate, a fact that was explained by quantum mechanics according to which the average acceleration of the delocalized electron is zero.