He Bohr's atomic model is a representation of the atom proposed by the Danish physicist Neils Bohr (1885-1962). The model states that the electron moves in orbits at a fixed distance around the atomic nucleus, describing a uniform circular motion. Orbits - or energy levels, as he called them - are of different energy.
Each time the electron changes orbit, it emits or absorbs energy in fixed quantities called"quanta". Bohr explained the spectrum of light emitted (or absorbed) by the hydrogen atom. When an electron moves from one orbit to another towards the nucleus there is a loss of energy and light is emitted, with characteristic wavelength and energy.
Atomic model of Bohr.
Bohr numbered the energy levels of the electron, considering that the closer the electron is to the nucleus, the lower its energy state. In this way, the farther away the electron is from the nucleus, the higher the energy level number will be and, therefore, the energy state will be higher.
Index
- 1 Main characteristics
- 1.1 It is based on other models and theories of the time
- 1.2 Experimental evidence
- 1.3 Electrons exist in energy levels
- 1.4 Without energy there is no movement of the electron
- 1.5 Number of electrons in each layer
- 1.6 The electrons rotate in circular orbits without radiating energy
- 1.7 Orbits allowed
- 1.8 Energy emitted or absorbed in jumps
- 2 Postulates of the Bohr atomic model
- 2.1 First postulate
- 2.2 Second postulate
- 2.3 Third postulate
- 3 Diagram of energy levels for hydrogen atoms
- 4 The 3 main limitations of the Bohr model
- 5 References
Main characteristics
Bohr's model characteristics are important because they determined the path towards the development of a more complete atomic model. The main ones are:
It is based on other models and theories of the time
Bohr's model was the first to incorporate quantum theory supported by the atomic model of Rutherford and ideas taken from the photoelectric effect of Albert Einstein. In fact Einstein and Bohr were friends.
Experimental evidence
According to this model, atoms absorb or emit radiation only when the electrons jump between the permitted orbits. German physicists James Franck and Gustav Hertz obtained experimental evidence of these states in 1914.
Electrons exist in energy levels
Electrons surround the nucleus and exist at certain energy levels, which are discrete and are described in quantum numbers.
The energy value of these levels exists as a function of a number n, called the main quantum number, which can be calculated with equations that will be detailed later on.
Without energy there is no movement of the electron
According to this model, without energy there is no movement of the electron from one level to another, just as without energy it is not possible to lift an object that has fallen or separate two magnets.
Bohr suggested the quantum as the energy required by an electron to pass from one level to another. He also stated that the lowest energy level occupied by an electron is called the"ground state". The"excited state"is a more unstable state, the result of the passage of an electron to a higher energy orbital.
Number of electrons in each layer
The electrons that fit in each layer are calculated with 2n 2
The chemical elements that are part of the periodic table and that are in the same column have the same electrons in the last layer. The number of elecrones in the first four layers would be 2, 8, 18 and 32.
The electrons rotate in circular orbits without radiating energy
According to Bohr's First Postulate, electrons describe circular orbits around the atom's nucleus without radiating energy.
Orbits allowed
According to Bohr's Second Postulate, the only allowed orbits for an electron are those for which the angular momentum L of the electron is an integer multiple of the Planck constant. Mathematically it is expressed thus:
Energy emitted or absorbed in jumps
According to the Third Postulate, the electrons would emit or absorb energy in the jumps from one orbit to another. In the jump of orbit a photon is emitted or absorbed, whose energy is represented mathematically:
Postulates of the Bohr atomic model
Bohr gave continuity to the planetary model of the atom, according to which the electrons revolved around a positively charged nucleus, as well as the planets around the Sun.
However, this model challenges one of the postulates of classical physics. According to this, a particle with an electrical charge (like the electron) that moves in a circular path, should lose energy continuously by emission of electromagnetic radiation. When losing energy, the electron would have to follow a spiral until falling in the nucleus.
Bohr then assumed that the laws of classical physics were not the most indicated to describe the stability observed in atoms and he presented the following three postulates:
First postulate
The electron spins around the nucleus in circling orbits, without radiating energy. In these orbits the orbital angular momentum is constant.
For the electrons of an atom only orbits of certain radii are allowed, corresponding to certain defined energy levels.
Second postulate
Not all orbits are possible. But once the electron is in an orbit that is allowed, it is in a state of specific and constant energy and does not emit energy (stationary energy orbit).
For example, in the hydrogen atom the energies allowed for the electron are given by the following equation:
In this equation the value -2.18 x 10 -18 is the Rydberg constant for the hydrogen atom, and n = quantum number can take values from 1 to ∞.
The electron energies of a hydrogen atom that are generated from the above equation are negative for each of the values of n. As n increases, the energy is less negative and, therefore, increases.
When n is large enough-for example, n = ∞-the energy is zero and represents that the electron has been released and the ionized atom. This state of zero energy harbors a greater energy than states with negative energies.
Third postulate
An electron can change from a stationary energy orbit to another by emitting or absorbing energy.
The energy emitted or absorbed will be equal to the energy difference between the two states. This energy E is in the form of a photon and is given by the following equation:
E = h ν
In this equation E is the energy (absorbed or emitted), h is the Planck constant (its value is 6.63 x 10 -3. 4 joule-seconds [J-s]) and ν is the frequency of light, whose unit is 1 / s.
Diagram of energy levels for hydrogen atoms
The Bohr model was able to satisfactorily explain the spectrum of the hydrogen atom. For example, in the range of wavelengths of visible light, the emission spectrum of the hydrogen atom is as follows:
Let's see how you can calculate the frequency of some of the observed light bands; for example, the color red.
Using the first equation and substituting n for 2 and 3 you get the results that appear in the diagram.
That is to say:
For n = 2, E 2 = -5.45 x 10 -19 J
For n = 3, E 3 = -2.42 x 10 -19 J
It is then possible to calculate the energy difference for the two levels:
ΔE = E 3 - E 2 = (-2.42 - (- 5,45)) x 10 - 19 = 3.43 x 10 - 19 J
According to the equation explained in the third postulate ΔE = h ν. Then, you can calculate ν (frequency of light):
ν = ΔE / h
That is to say:
ν = 3.43 x 10 -19 J / 6.63 x 10 -3. 4 J-s
ν = 4.56 x 10 14 s -1 or 4.56 x 10 14 Hz
Being λ = c / ν, and the speed of light c = 3 x 10 8 m / s, the wavelength is given by:
λ = 6,565 x 10 - 7 m (656.5 nm)
This is the value of the wavelength of the red band observed in the spectrum of hydrogen lines.
The 3 main limitations of the Bohr model
1- It adapts to the spectrum of the hydrogen atom but not to the spectra of other atoms.
2 - The wave properties of the electron are not represented in the description of this as a small particle that revolves around the atomic nucleus.
3- Bohr fails to explain why classical electromagnetism does not apply to his model. That is, why electrons do not emit electromagnetic radiation when they are in a stationary orbit.
References
- Brown, T. L. (2008). Chemistry: the central science. Upper Saddle River, NJ: Pearson Prentice Hall
- Eisberg, R., & Resnick, R. (2009). Quantum physics of atoms, molecules, solids, nuclei, and particles . New York: Wiley
- Atomic model of Bohr-Sommerfeld. Retrieved from: fisquiweb.es
- Joesten, M. (1991). World of chemistry Philadelphia, Pa.: Saunders College Publishing, pp.76-78.
- Modèle de Bohr de l'atome d'hydrogène. Retrieved from fr.khanacademy.org
- Izlar, K. Retrospective sur l'atome: le modèle de Bohr a cent ans. Retrieved from: home.cern