The Bohr Model of the Atom

Niels Bohr in 1913 formulated the basic propositions of his theory in the form of postulates (a postulate is a statement accepted without proof) given below:

An electron can revolve about a nucleus not in any random orbit, but only in certain definite circular orbits. The latter were called stationary orbits.

When travelling in a stable orbit, an electron emits no electro­magnetic energy.

Emission occurs when an electron makes a transition (jumps) from one stationary orbit to another. This is attended by the emission or absorption of a quantum of electromagnetic radiation whose energy equals the difference between the energy" of the atom in the final and that in the initial states.

If we denote the initial energy of an atom when an electron is in an orbit farther from the nucleus by E_in, and the final energy of the atom for the orbit closest to the nucleus by E_f, then the energy of a quaiitum emitted when an electron makes the transition will equal the difference

E = E_in — E_f

According to the first Bohr`s postulate we can obtain that the electron is only allowed to be in certain orbits. In other words, its angular momentum L = mvr is quantized, viz.

(n - integer) or (1)

From the Rutherford model follows that the centrifugal force produced owing to rotation of the electrons around the nucleus is balanced by the force of electrostatic attraction of the electrons (Coulomb's law) to the oppositely charged nucleus.

(2)

If both parts of the last equation (2) are divided on the previous one, we shall receive the expression of the speed of electron in atom:

(3)

Let's substitute the expression for the speed of an electron (3) in the equation (1):

mvr

From here we obtain expression for the radius of an electron orbit and it possible to calculate the radius of the first energy level (first Bohr orbit):

(4)

So, r₁ =0.528×10^-8cm; r = n² ×0.528×10^-8cm and r₁ : r₂ : r₃ = 1 : 4 : 9

Bohr's theory not only explained the physical nature of atomic spectra to be the result of transition of an atom's electrons from one set of stationary orbits to others, but also for the first time allowed calculation of the spectra. Bohr's calculation of the spectrum of the simplest atom—the hydrogen atom—gave brilliant results: the computed position of the spectral lines in the visible part of the spectrum coincided excellently with their actual position in the spectrum. These lines were found to correspond to a transition of an electron from the more remote orbits to the second one from the nucleus.

The triumph of Bohr's theory cannot nevertheless be considered complete. A number of questions associated with Bohr's postulates themselves remained unclear, for example: where is an electron in the process of its transition from one orbit to another? This theory could not explain some important spectral characteristics of many-electron atoms and even of the hydrogen atom. For instance, the reason why the lines in the atomic spectrum of hydrogen have different intensities remained unclear.

Bohr's theory was nevertheless an important step in the development of the concepts of the atomic structure. Like Planck's and Einstein's hypothesis of light quanta (photons), it showed that the laws of nature holding for large bodies—objects of the macroworld— cannot be extended automatically to negligibly small objects of the micro-world such as atoms, electrons, and photons. This is exactly why the problem appeared of developing a new physical theory suitable for an uncontradictory description of the properties and beha­viour of objects of the microworld. For macroscopic bodies, the conclusions of this theory must coincide with those of classical mechanics and electrodynamics (the so-called correspondence principle advanced by Bohr).

This problem was solved in the twenties of the 20th century after the appearance and development of a new branch of theoretical physics—quantum or wave mechanics.