Physics

Bohr Atomic Model


The atom has always been studied through models proposed by scientists. Each model brought hypotheses based on theoretical formulations and experimental results obtained by their respective authors, remaining valid until it presented flaws in the explanation of the phenomena. If so, researchers should propose new models or adaptations to the theories already developed.

In 1911 Ernest Rutherford proposed a model that described the atom as a planetary system, in which there was a positively charged central nucleus and orbiting electrons around it. Although important, Rutherford's model did not correctly explain some phenomena. According to Maxwell's theory, any accelerated charge should emit electromagnetic radiation, losing energy. Since an electron of the Rutherford atom described a circular orbit and thus had centripetal acceleration, it should emit radiation permanently, reducing its energy level. Thus, it should describe a spiraling path until it falls into the nucleus, which did not occur, since the electrospheres of atoms are stable.

Also, there is another problem with Rutherford's model. According to Maxwell, the radiation emitted by the electron has the same frequency of motion. Thus, since the frequency of electron motion should vary continuously as it travels to the nucleus, the electron should also continuously emit radiation of varying frequency. However, radiation emitted by an atom should only have frequencies of certain values, unlike thermal radiation emitted by a body, which has a continuous spectrum.

Because of these inconsistencies, Niels Bohr developed a new theory based on quantum ideas. Bohr inferred that for an atom's electrosphere to be stable, the electrons of that atom must assume certain energy levels, called steady states or quantum, each of them corresponding to a particular energy. He postulated that in a steady state the atom emitted no radiation, so its electrosphere remained stable.

Gustav Hertz and James Franck the following year confirmed the existence of steady states. The steady state, whose electrons are at the lowest energy levels, is called the Fundamental State; the other allowed states are called excited states. This means that only the ground state and the other excited states are allowed - any other states are prohibited.

Considering the particular case of hydrogen, which consists of only one electron, the energy levels can be obtained by the expression below:

Where the main quantum number is symbolized by the letter n (= 1, 2, 3…) and Eno is the energy corresponding to each quantum number.

Importantly, n = 1 corresponds to the ground state of energy. In addition, the energy values ​​are negative, meaning that the electron must receive energy to reach the level, either ceasing to interact with the nucleus at that time, or losing its bond with the atom.

Bohr also postulated that every atom, moving from one steady state to another, emits or absorbs a quantum of energy exactly equal to the difference between the energies corresponding to those states. This result cannot be explained by classical electromagnetic theory, since, according to it, the frequency of emitted radiation is related to the frequency of electron movement. We now know that this is not correct, since the frequency of emitted radiation relates only to the energy difference between the initial and final states.

According to Bohr, electrons describe circular paths around a positive nucleus due to the force of attraction given by Coulomb's Law which in this case is the centripetal force of motion. The radii of these trajectories can only assume certain well-determined values. For hydrogen, for example, the permitted values ​​for the rays are given by the expression below:

Where:

n = quantum number (n = 1, 2, 3…);

rno = radius of orbit corresponding to quantum number n;

r1 = radius corresponding to the ground energy state, given by:

Where:

h = Planck constant (h = 6.63x10-34J s);

K = electrostatic vacuum constant (K = 9x109 Nm² / C²);

Z = atomic number of the chemical element;

e = electron charge (K = 1.6x10-19 Ç);

m = electron mass (e = 9.1 x10-31 kg).