6.2 The Bohr Model

In atomic physics, the Rutherford–Bohr model or Bohr model, presented by Niels Bohr and Ernest Rutherford in 1913, is a system consisting of a small, dense nucleus surrounded by orbiting electrons—similar to the structure of the Solar System, but with attraction provided by electrostatic forces in place of gravity.

Development of the Bohr Model

The Bohr model was an improvement on the earlier cubic model (1902), the plum-pudding model (1904), the Saturnian model (1904), and the Rutherford model (1911). Since the Bohr model is a quantum-physics-based modification of the Rutherford model, many sources combine the two: the Rutherford–Bohr model.

Although it challenged the knowledge of classical physics, the model’s success lay in explaining the Rydberg formula for the spectral emission lines of atomic hydrogen. While the Rydberg formula had been known experimentally, it did not gain a theoretical underpinning until the Bohr model was introduced. Not only did the Bohr model explain the reason for the structure of the Rydberg formula, it also provided a justification for its empirical results in terms of fundamental physical constants.

Although revolutionary at the time, the Bohr model is a relatively primitive model of the hydrogen atom compared to the valence shell atom. As an initial hypothesis, it was derived as a first-order approximation to describe the hydrogen atom. Due to its simplicity and correct results for selected systems, the Bohr model is still commonly taught to introduce students to quantum mechanics. A related model, proposed by Arthur Erich Haas in 1910, was rejected. The quantum theory from the period between Planck’s discovery of the quantum (1900) and the advent of a full-blown quantum mechanics (1925) is often referred to as the old quantum theory.

Early planetary models of the atom suffered from a flaw: they had electrons spinning in orbit around a nucleus—a charged particle in an electric field. There was no accounting for the fact that the electron would spiral into the nucleus. In terms of electron emission, this would represent a continuum of frequencies being emitted since, as the electron moved closer to the nucleus, it would move faster and would emit a different frequency than those experimentally observed. These planetary models ultimately predicted all atoms to be unstable due to the orbital decay. The Bohr theory solved this problem and correctly explained the experimentally obtained Rydberg formula for emission lines.

The Bohr model shows that the electrons in atoms are in orbits of differing energy around the nucleus (think of planets orbiting around the sun). Bohr used the term energy levels (or shells) to describe these orbits of differing energy. … The energy level an electron normally occupies is called its ground state.

Figure 6.14 Bohr’s Orbit

Ref: Commons.wikimedia.org/

Chemistry 2.5 Bohr Model of the Atom

The Bohr Model can relate and explain the Rydberg formula for emission spectra lines of several atoms especially of hydrogen atom. The model is based on the fact that electrons orbits around the nucleus in a circular mode at very specific and discrete distances. Each orbit is associated with specific, definite and discrete energy. Such orbit is called energy shell or just energy level.

The orbits are stable and electrons orbiting around the nucleus does not yield a radiation or energy loss as the classical electromagnetic theory assumes.

Figure 6.15 Rutherford–Bohr model of the hydrogen atom

Reference: https://courses.lumenlearning.com/introchem/chapter/the-bohr-model/

Properties of Electrons under the Bohr Model

In 1913, Bohr suggested that electrons could only have certain classical motions:

• Electrons in atoms orbit the nucleus.
• The electrons can only orbit stably, without radiating, in certain orbits (called by Bohr the “stationary orbits”) at a certain discrete set of distances from the nucleus. These orbits are associated with definite energies and are also called energy shells or energy levels. In these orbits, an electron’s acceleration does not result in radiation and energy loss as required by classical electromagnetic theory.
• Electrons can only gain or lose energy by jumping from one allowed orbit to another, absorbing or emitting electromagnetic radiation with a frequency (ν) determined by the energy difference of the levels according to the Planck relation.

Behavior of Electrons: Part 3, The Bohr Model of the Atom – YouTube We combine our new found knowledge of the nature of light with Bohr’s atomic theory.

Behavior of Electrons: Part 3, The Bohr Model of the Atom

Bohr’s model is significant because the laws of classical mechanics apply to the motion of the electron about the nucleus only when restricted by a quantum rule. Although Rule 3 is not completely well defined for small orbits, Bohr could determine the energy spacing between levels using Rule 3 and come to an exactly correct quantum rule—the angular momentum L is restricted to be an integer multiple of a fixed unit:

∆E= E₂-E₁ =h.ν, h= Planck’s constant, 6.626 *10^-34 J.s

E₂ and E₁ are the corresponding energy levels of the orbits. Orbits are denoted by n. n = 1, 2, 3, … is called the principal quantum number. The lowest value of n is 1; this gives a smallest possible orbital radius of 0.0529 nm, known as the Bohr radius. Once an electron is in this lowest orbit, it can get no closer to the proton. Starting from the angular momentum quantum rule, Bohr was able to calculate the energies of the allowed orbits of the hydrogen atom and other hydrogen-like atoms and ions.

Figure 6.16 Energy Transition in Bohr’s Orbit

Ref: Commons.wikimedia.org/

The Correspondence Principle

Bohr atom model postulate had corrected the Rutherford’s atom’s model. Bohr postulated that the electrons can orbit around the nucleus without radiating any energy and each orbit has its own definite energy. The stable orbit has discrete distance from the nucleus.

Furthermore, each orbit will have very distinct angular momentum which is an integer multiple of the reduced Planck constant with the principle quantum number n = 1, 2, 3, 4 etc.

In addition, Bohr was dependent on the old classical electromagnetic theory of Maxwell theory and one of weakest point of Bohr’s model was that the Bohr himself did not believe in the concept of photons as explained by Einstein.

Maxwell theory states that the frequency ν of old classical radiation is equal to the rotation frequency of the electron in its orbit, with harmonics at integer multiples of this frequency. Bohr model predicted that the transfer of the electron from one level to another will acquire specific energy levels E_n and E_n−k where k is much smaller than n. F

In case of  larger values of n (Rydberg states), the two orbits involved in the emission process have nearly the same rotation frequency, so that the classical orbital frequency is clear. But for small n (or large k), the radiation frequency has clear explanation.

Reference: https://en.wikipedia.org/wiki/Bohr_model

Bohr’s Model of an Atom | Atoms and Molecules | Don’t Memorise

Bohr Model of an Atom