BOHR'S ATOMIC MODEL: CHARACTERISTICS AND POSTULATES - PHYSICAL - 2025

The Bohr atomic model is a representation of the atom proposed by the Danish physicist Neils Bohr (1885-1962). The model establishes that the electron travels in orbits at a fixed distance around the atomic nucleus, describing a uniform circular motion. The orbits - or energy levels, as he called them - are of different energy.

Every time the electron changes its orbit, it emits or absorbs energy in fixed amounts 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.

Source: wikimedia.org. Author: Sharon Bewick, Adrignola. Illustration of Bohr's atomic model. Proton, orbit and electron.

Bohr numbered the energy levels of the electron, considering that the closer the electron is to the nucleus, the lower its energy state. Thus, the further away the electron is from the nucleus, the number of the energy level will be greater and, therefore, the energy state will be greater.

Main features

The Bohr model features are important because they determined the path to the development of a more complete atomic model. The main ones are:

It is supported by other models and theories of the time

Bohr's model was the first to incorporate quantum theory, based on Rutherford's atomic model and on ideas taken from Albert Einstein's photoelectric effect. In fact Einstein and Bohr were friends.

Experimental evidence

According to this model, atoms absorb or emit radiation only when electrons jump between allowed orbits. The German physicists James Franck and Gustav Hertz obtained experimental evidence for 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 value of the energy of these levels exists as a function of a number n, called the principal quantum number, which can be calculated with equations that will be detailed later.

Without energy there is no movement of the electron

Source: wikimedia.org. Author: Kurzon

The upper illustration shows an electron making quantum leaps.

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 a fallen object or to separate two magnets.

Bohr suggested the quantum as the energy required by an electron to pass from one level to another. He also established that the lowest energy level that an electron occupies 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 shell

The electrons that fit in each shell are calculated with 2n ²

Chemical elements that are part of the periodic table and that are in the same column have the same electrons in the last shell. The number of elecrons in the first four layers would be 2, 8, 18, and 32.

Electrons rotate in circular orbits without radiating energy

According to Bohr's First Postulate, electrons describe circular orbits around the nucleus of the atom without radiating energy.

Orbits allowed

According to Bohr's Second Postulate, the only orbits allowed for an electron are those for which the angular momentum L of the electron is an integer multiple of Planck's constant. Mathematically it is expressed like this:

Energy emitted or absorbed in jumps

According to the Third Postulate, electrons would emit or absorb energy in jumps from one orbit to another. In the orbit jump, a photon is emitted or absorbed, whose energy is represented mathematically:

Bohr's atomic model postulates

Bohr continued the planetary model of the atom, according to which electrons revolved around a positively charged nucleus, just like the planets around the Sun.

However, this model challenges one of the postulates of classical physics. According to this, a particle with an electric charge (such as the electron) that moves in a circular path, should continuously lose energy by emission of electromagnetic radiation. When losing energy, the electron would have to follow a spiral until it fell into the nucleus.

Bohr then assumed that the laws of classical physics were not the most suitable for describing the observed stability of atoms and put forward the following three postulates:

First postulate

The electron goes around the nucleus in orbits that draw circles, 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 previous 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 atom ionized. This zero energy state harbors higher energy than negative energy states.

Third postulate

An electron can change from one stationary energy orbit to another by emission or absorption of energy.

The energy emitted or absorbed will be equal to the difference in energy 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 Planck's constant (its value is 6.63 x 10 ^-34 joule-seconds) and ν is the frequency of light, whose unit is 1 / s.

Energy Level Diagram for Hydrogen Atoms

The Bohr model was able to satisfactorily explain the spectrum of the hydrogen atom. For example, in the wavelength range of visible light, the emission spectrum of the hydrogen atom is as follows:

Let's see how the frequency of some of the observed light bands can be calculated; for example, the color red.

Using the first equation and substituting 2 and 3 for n, the results shown in the diagram are obtained.

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. So, 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 ^-34 Js

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 wavelength value of the observed red band in the hydrogen line spectrum.

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 it as a small particle that revolves around the atomic nucleus.

3- Bohr cannot 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.

Articles of interest

Schrödinger's atomic model.

De Broglie atomic model.

Chadwick's atomic model.

Heisenberg atomic model.

Perrin's atomic model.

Thomson's atomic model.

Dalton's atomic model.

Dirac Jordan atomic model.

Atomic model of Democritus.

Sommerfeld atomic model.

References

1. Brown, TL (2008). Chemistry: the central science. Upper Saddle River, NJ: Pearson Prentice Hall
2. Eisberg, R., & Resnick, R. (2009). Quantum physics of atoms, molecules, solids, nuclei, and particles. New York: Wiley
3. Bohr-Sommerfeld atomic model. Recovered from: fisquiweb.es
4. Joesten, M. (1991). World of chemistry. Philadelphia, Pa.: Saunders College Publishing, pp.76-78.
5. Model of Bohr de l'atome d'hydrogène. Recovered from fr.khanacademy.org
6. Izlar, K. Rétrospective sur l'atome: le modèle de Bohr a cent ans. Recovered from: home.cern