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# Bohr Model

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 Sub Topics Hydrogen the simplest of all elements, was investigated most extensively both experimentally and theoretically. As long ago as 1885, Balmer succeeded in obtaining a simple relationship among the wave numbers of the lines in the visible region of the hydrogen spectrum. The first quantitative correct derivation of the Balmer formula on the basis of an atomic model was given by Bohr (1913), in his theory of the hydrogen atom. Those theory has played such an important role in the development of atomic physics that even though it has been modified and extended by the later developments in quantum mechanics, it will be worthwhile to present the original simplified theory.In 1913, Niels Bohr proposed a model for the hydrogen atom which retained the earlier nuclear model of Rutherford but made further stipulations as to the behavior of the electron. A dramatic explanation of the Rydberg spectral expression resulted.

## Bohr Model Definition

"The Bohr model describes an atom as a nucleus with electrons in orbit around the nucleus. The orbits in the Bohr model are circular." In Bohr model an electron is regarded as a charged particle moving in well-defined circular orbits about the nucleus. The wave character of the electron is not considered in Bohr model.
Bohr model of the hydrogen atom therefore not only ignores dual behavior of matter but also contradicts Heisenberg uncertainty principle. In view of these inherent weaknesses in the Bohr model there was no point in extending Bohr model to other atoms.

## Bohr Model Explanation

Bohr discovered that electrons orbit the nucleus of an atom at set distances, changing levels only when energy is lost or gained and emitting or absorbing radiation in the process.

Bohr model is an early model of atomic structure in which electrons circulate around the nucleus in discrete stable orbits with different energy levels. This model was the first to predict and explain the atomic spectrum of the hydrogen atom, which arises as the electron jumps from one orbit to another orbit of lower energy, giving off electromagnetic radiation of predictable frequencies. Later models of atomic structure abandoned the idea of circular orbits, and explained the stable orbits as standing waves.

How to Make a Bohr Model?

Bohr based his investigation on Max Plank ides. He imagined he electron orbiting the nucleus unless it was disturbed by some outside force, when it jumped to a different energy level. A packet of energy was either gained or lost.

The Bohr model of the atom was discrete or quantized, and such views formed the basis of the branch of models in physics that has come to known as quantum mechanics.

## Bohr Models for all Elements

Bohr specified each orbit with an integer n called the orbital quantum number. The higher the quantum number, the greater the distance between the electron and the nucleus and higher the electrons energy.

Bohr model is a theory for the way electrons behave in atoms that explains the periodic law. The Bohr model for some of the atoms are listed below.

 S.No Element Bohr model 1 Bohr Model of Hydrogen 2 Bohr Model of Carbon 3 Bohr Model of Oxygen 4 Bohr Model of Sodium 5 Bohr Model of Neon 6 Bohr Model of Helium 7 Bohr Model of Lithium 8 Bohr Model of Magnesium 9 Bohr Model of Nitrogen 10 Bohr Model of Calcium 11 Bohr Model of Chlorine 12 Bohr Model of Potassium 13 Bohr Model of Aluminum 14 Bohr Model of Sulfur 15 Bohr Model of Boron 16 Bohr Model of Gold 17 Bohr Model of Argon 18 Bohr Model of Iron 19 Bohr Model of Copper

## Spectrum of Hydrogen Atom

An atom of hydrogen consists of just one proton with one surrounding electron. The emission spectrum of hydrogen is relatively simple compared to those of other elements. The complete spectrum of hydrogen consists of separate series of distinct wavelength concentrated in the ultraviolet, visible and infrared regions of the electromagnetic spectrum.

The six series found are named after their discoveries. In order of increasing wavelength they are the Lyman series (ultraviolet), Balmer series (visible), Paschen, Brackett, Pfund and Humphreys series (infrared).

Each of these series is called a line spectrum because the film record from the spectrometer appears as a pattern of separate thin vertical lines.

## Bohr Electron Model

Bohr proposed that electrons could only orbit at specific fixed distances from the nucleus. Those fixed distances then corresponded to specific fixed energies for the electron. Bohr specified each orbit with an integer n called the orbits quantum number.

The higher the quantum number is the greater is the distance between the electron and the nucleus and the higher is the electrons energy. Bohr also stipulated that the orbits could only hold a maximum number of electrons determined by the value of n as follows.
1. Bohr orbit with n = 1 holds a maximum of two electrons
2. Bohr orbit with n = 2 holds a maximum of eight electrons
3. Bohr orbit with n = 3 holds a maximum of eight electrons
In an atom an electron occupies the lowest energy orbit that is available. The Bohr model electron shells is given below.

## Bohr Atomic Structure

Bohr proposed a theory of atomic structure for the interpretation of atomic spectra. The atom had the extra nuclear electrons revolving around the nucleus in definite orbits. These orbits were assigned principal quantum numbers 1, 2, 3,...n counting from the nucleus.

When an electron absorbs a definite increment of energy it is promoted to an orbit of higher energy and when it falls back to the original orbit, it emits radiation energy. The energy of the various levels in the atom can be related to the frequency of radiation that is emitted from or absorbed by the atom.

The Bohr model equation is given by

$\Delta E = E_{2} - E_{1} = h\nu$

$\Delta E = \frac{hc}{\lambda}$

The energy of an electron in an orbit is given by

$E = \frac{-2\pi^{2}Z^{2}me^{4}}{n^{2}h^{2}}$

The Bohr atomic model picture is given below.

## Niels Bohr Atomic Theory

In 1913 Neils Bohr a danish physicist provided an explanation for the occurrence of line spectra, such as those described by the Rydberg equation. Through an interesting combination of classical and quantum theory, Bohr was able to overcome the drawbacks in Rutherford's model. He suggested that the electrons in an atom revolve around the nucleus of an atom only in certain discrete orbits with no other orbits being possible.

## Bohr Model Examples

The Bohr model problems are given below.

### Solved Examples

Question 1: Calculate the minimum energy required to remove the electron from the hydrogen atom in its ground state.
Solution:

Removing the electron from hydrogen atom in its ground state corresponds to taking the electron from

ninitial = 1 to nfinal = $\infty$
Thus

$\Delta{E} = -2.178 \times 10^{-18}J [\frac{1}{n_{final}^{2}} - \frac{1}{n_{initial}^{2}}]$

= 2.178 $\times$ 10-18J

Thus the energy required to remove the electron from a hydrogen atom in its ground state is 2.178 $\times$ 10-18J

Question 2: Considering Bohr model of the hydrogen atom, what process is taking place in the atom when t emits light of a definite wavelength?
Solution:

An electron is making a transition from a higher to a lower principle energy level,

such as from n = 4 $\rightarrow$ n = 2 $\rightarrow$ n = 1.

Each energy level is fixed and the energy of the light emitted equals the difference in energy between the two levels.