Modern Physics

# Postulates of Bohr Atomic Model

Niels Bohr  ( 10/7/1885 – 11/18/1962 ) was a Danish physicist and Nobel Prize known for his (fundamental) contribution to the development of atomic theory and quantum mechanics.

Notable findings on the  structure of the atom  include three famous postulates of Bohr atomic model based  Rutherford atomic model, which applied the latest theoretical and experimental findings on the nature of the subject: the atomic theory Planck, the photoelectric effect and the atomic spectra

## Bohr’s theory of the  hydrogen atom

The Rutherford model of the atom and the experimental formula of atomic spectra helped Bohr is solving the problem of atomic structure. In 1913 he proposed a model for the structure of a hydrogen atom based on his experimental observations.

## Postulates of Bohr atomic model

Neil Bohr based his theory of hydrogen atom on the following three postulates.

• ### The postulates of stationary states

Bohr assumed that hydrogen atom can exist for a long time without radiating in any one of the numbers of stationary states of well-defined energy.

• ### Angular momentum postulate

Only those orbits around the nucleus are possible for which angular momentum is the integral multiple of h/2π  i.e:

mvr =nh/2π

In other words orbits are quantized.

• ### The frequency postulate

Bohr assumed that hydrogen atom can emit or absorb radiation only when the atom changes from one of its stationary states to another.If an atom changes from initial state of energy En to a final state of lower energy Em, then the energy of the emitted photon is given by:

hν = En   -Em  ——————–(1)

## Derivation of Bohr’s theory

The hydrogen atom is the simplest of the atoms because it contains only one proton in its nucleus and one electron revolving around it in the first orbit. We take central charge to be ‘Ze’ where ‘Z’ is the atomic number and z=1 for the hydrogen atom. Suppose M is the nuclear mass and me is the mass of an electron. The force of attraction between the nucleus and the electron provides a centripetal force to the electron to move in a circular orbit. Hence we can write:

#### Bohr atomic model failures

Bohr’s model was a major stage towards the development of the modern quantum theory of the atom, with a correct description of the nature of the electron’s orbits. But, Bohr’s postulates are clearly a mixture of ideas of classical physics with the ideas of quantization initially introduced by Planck and Einstein.

On the one hand the electron moves in a circular orbit and obeys the equations of motion of classical mechanics, but on the other hand a magnitude such as the angular momentum that in classical mechanics can have a continuum of values, in a permitted stationary orbit the electron must satisfy a non-classical quantitative condition of the orbital angular momentum, which can only reach a series of discrete values ​​(a quantum idea).

On the other hand, the electron being in orbit obeys a law of classical electromagnetism that is the coulomb law, but on the contrary, it does not comply with the classical law that would guarantee the radiation of energy by an accelerated charge. Ultimately, these postulates establish that the classical physical laws that are valid for macroscopic systems cease to be so in the world of microscopic systems.

## The defects of the Bohr model were evidenced as:

The model fails to provide an explanation of why certain spectral lines in the hydrogen spectrum are brighter than others, that is, it did not provide a satisfactory way to calculate the probability of transition from one quantum state to another. That is, the model has no mechanism to calculate the probabilities of transition between stationary states.

Bohr’s model treats the electron as if it were a miniature planet, with a defined radius of orbit and momentum. This assumption is a direct violation of the uncertainty principle, a key principle in Quantum Mechanics which dictates that the quantum world position and momentum cannot be determined simultaneously.

Bohr’s model provides a basic conceptual model of electron and energy orbits. Spectrum details and charge distribution require quantum mechanics calculations that use the Schrödinger equation.

However, Bohr introduced an important principle called the principle of correspondence that states that in the limit of large orbits and energies (in the region of large quantum numbers eg $n$) quantum calculations must agree with classical calculations or in other words if Modifications of classical physics are made to describe the submicroscopic world when the results of these are extended to the macroscopic world, the results must be in accordance with the classical laws of physics that have been verified on the ordinary scale of the everyday world.

Although the details of Bohr’s atomic model have been supplanted by modern quantum mechanics, its frequency condition and the principle of correspondence still remain an essential feature of the new quantum theory.

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