The Bohr atomic model is the Danish physicist Niels Bohr's (1885-1962) conception of the structure of the atom, published in 1913. In the Bohr atom, the electrons around the nucleus occupy only certain allowed orbits, thanks to a restriction called quantization.
For Bohr, the image of the atom as a miniature solar system, with electrons orbiting around the nucleus, was not entirely consistent with the fact that electric charges, when accelerated, radiate energy..
Such an atom would not be stable, because it would end up collapsing sooner or later because the electrons would spiral towards the nucleus. And by then, the characteristic light patterns that hydrogen and other gases emit when heated had been known for 50 years..
The pattern or spectrum consists of a series of bright lines of certain very specific wavelengths. And the hydrogen atom does not collapse from emitting light.
To explain why the atom is stable despite being able to radiate electromagnetic energy, Bohr proposed that angular momentum could only adopt certain values, and therefore energy as well. This is what is meant by quantization.
Accepting that the energy was quantized, the electron would have the necessary stability not to rush towards the nucleus destroying the atom..
And the atom only radiates light energy when the electron transitions from one orbit to another, always in discrete quantities. In this way, the presence of emission patterns in hydrogen is explained..
Bohr thus composed a vision of the atom by integrating familiar concepts from classical mechanics with newly discovered ones, such as Planck's constant, the photon, the electron, the atomic nucleus (Rutherford had been Bohr's mentor), and the aforementioned spectra of issue.
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Bohr's atomic model assumes that the electron moves in a circular orbit around the nucleus by the action of Coulomb's electrostatic attractive force and proposes that the angular momentum of the electron is quantized.
Let's see how to integrate both concepts in mathematical form:
Let L be the magnitude of the angular momentum, m the mass of the electron, v the speed of the electron, and r the radius of the orbit. To calculate L we have:
L = m⋅r⋅v
Bohr proposed that L was equal to integer multiples of the constant h / 2π, where h is the Planck's constant, introduced a short time ago by the physicist Max Planck (1858-1947) when solving the problem of the energy emitted by a black body, a theoretical object that absorbs all the incident light.
Its value is h = 6.626 × 10−34 J ・ s, while a h / 2π is denoted as ħ, what is read "H bar".
Therefore, the angular momentum L remains:
m⋅r⋅v = nħ, with n = 1,2, 3 ...
And from this condition the radii of the orbits allowed for the electron are deduced, as we will see below.
In what follows we will assume the simplest of the atoms: hydrogen, which consists of a single proton and an electron, both with a charge of magnitude e.
The centripetal force that keeps the electron in its circular orbit is provided by electrostatic attraction, whose magnitude F is:
F = ketwo/ rtwo
Where k is the electrostatic constant of Coulomb's law and r the electron-proton distance. Knowing that in a circular motion the centripetal acceleration atc is given by the ratio between the square of the speed and the distance r:
toc = vtwo / r
By Newton's second law, the net force is the product of the mass m and the acceleration:
mvtwo/ r = ketwo/ rtwo
Simplifying the radius r, we obtain:
m⋅vtwor = ketwo
Combining this expression with that of angular momentum we have a system of equations, given by:
1) mvtwor = ketwo
2) r = n ħ/ mv
The idea is to solve the system and determine r, the radius of the allowed orbit. A little elementary algebra leads to the answer:
r = (nħ)two / k⋅m⋅etwo
With n = 1, 2, 3, 4, 5 ...
For n = 1 we have the smallest of the radii, called Bohr radius toor with a value of 0.529 × 10−10 m. The radii of the other orbits are expressed in terms of toor.
In this way Bohr introduces the principal quantum number n, noting that the allowed radii are a function of Planck's constant, the electrostatic constant and the mass and charge of the electron.
Bohr skillfully combines Newtonian mechanics with new discoveries that were continually occurring during the second half of the nineteenth and early twentieth centuries. Among them the revolutionary concept of the "quantum", of which Planck himself claimed not to be very convinced.
By means of his theory, Bohr was able to satisfactorily explain the series of the hydrogen spectrum and predict energy emissions in the ultraviolet and infrared range, which had not yet been observed..
We can summarize its postulates as follows:
The electron revolves around the nucleus in a stable circular orbit, with uniform circular motion. The movement is due to the electrostatic attraction that the nucleus exerts on it.
The angular momentum of the electron is quantized according to the expression:
L = mvr = nħ
Where n is an integer: n = 1, 2, 3, 4 ..., which leads to the fact that the electron can only be in certain defined orbits, whose radii are:
r = (n ħ)two / k m etwo
Since the angular momentum is quantized, so is the energy E. It can be shown that E is given by:
The electron volt, or eV, is another unit for energy, widely used in atomic physics. The negative sign in the energy ensures the stability of the orbit, indicating that work would have to be done to separate the electron from this position..
While the electron is in its orbit it does not absorb or emit light. But when it jumps from a higher energy orbit to a lower one, it does..
The frequency f of the emitted light depends on the difference between the energy levels of the orbits:
E = hf = Einitial - Efinal
The Bohr model has certain limitations:
-It is only applied successfully to the hydrogen atom. Attempts to apply it to more complex atoms were unsuccessful.
-It does not answer why some orbits are stable and others are not. The fact that the energy in the atom was quantized worked very well, but the model did not provide a reason, and that was something that caused scientists discomfort..
-Another important limitation is that it did not explain the additional lines emitted by atoms in the presence of electromagnetic fields (Zeeman effect and Stark effect). Or why some spectrum lines were stronger than others.
-The Bohr model also does not consider relativistic effects, which it is necessary to take into account, since it was experimentally determined that electrons are capable of reaching speeds quite close to that of light in a vacuum..
-It assumes that it is possible to know precisely the position and velocity of the electron, but what is actually calculated is the probability that the electron occupies a certain position.
Despite its limitations, the model was very successful at the time, not only for integrating new discoveries with elements already known, but also because it raised new questions, making it clear that the path to a satisfactory explanation of the atom lay in quantum mechanics..
Schrödinger's atomic model.
Atomic de Broglie model.
Atomic model of Chadwick.
Heisenberg atomic model.
Atomic model of Perrin.
Thomson's atomic model.
Dalton's atomic model.
Dirac Jordan atomic model.
Atomic model of Democritus.
Atomic model of Leucippus.
Sommerfeld atomic model.
Current atomic model.
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