### Bohr’s Model of Atom

Neils Bohr founded the Institute of Theoretical Physics at the , now known as the Niels Bohr Institute, in 1920. He predicted the existence of a new zirconium-like element, which was named hafnium,after the Latin name for Copenhagen, where it was discovered. Later, the element Bohrium was named after him.

In September 1943, word reached Bohr that he was about to be arrested by the Germans, and he fled to Sweden. From there, he was flown to Britain, and later became part of the British mission to the Manhattan Project.

Bohr proposed the atomic model in 1913 according to which the electrons travel in circular orbits around the nucleus due to electrostatic force. It was actually the modification of Rutherfordâ€™s atomic model who predicted electronic cloud around a positively charged nucleus. Rutherfordâ€™s model however faced some technical difficulties when viewed in terms of classical mechanics. This model did not use orbits of fixed positions. The model was defective because according to classical mechanics the orbiting electron will lose energy and ultimately fall into nucleus. Also as the orbit will get smaller and smaller the frequency of the emitted radiation will increase, which is not seen in emission spectra. Such a model of an atom was not acceptable since it shows that all atoms are unstable which is not applicable.

Bohrs atomic model was also based on the classical mechanics but a *quantum concept* was introduced into it by stating that the electrons can revolve around the nucleus only in certain allowed circular paths. He postulated that:

1. Electrons revolve around the nucleus in circular orbits

2. The electronic orbits are fixed i.e. they can revolve around the nucleus at certain discrete set of distances (energy levels) having particular energies. Thus while orbiting the acceleration of electron does not result in the emission of radiation as by the classical electromagnets (quantum concept).

3. Electrons can only lose or gain energy by jumping from one energy level to other and the emission or absorbance of radiation is determined by the band gap between two levels.

Bohrs model was based upon Plancks quantum theory of radiation introduced by Max Planck in 1900 which stated that energy can only be emitted or absorbed in discrete amounts.

The energy difference between the electronic orbits can be found by using Planks Law equation which is:

*âˆ†E = E _{2} – E_{1}*

=

*hv*

Where *h* is Plancks’s constant and *v* is the frequency of radiation emitted. According to the postulate 3 the laws of classical mechanics were valid for the motion of electrons only when viewed in terms of quantum rule i.e. the electrons can only radiate a certain discrete amount* *of energy by jumping from one orbit to another. Thus the energy of the electron in an orbit is fixed and so is angular momentum. The angular momentum is an integral multiple of fixed unit given by:

*L = n h/2Ï€ = nÄ§*

Where *Ä§ = h/2Ï€ *and* *n = 1, 2, 3â€¦is a principal quantum number and its lowest value is 1. Bohr model was successfully applied to calculate the orbital energies of hydrogen and hydrogen like atoms.

**Electrons energy level of hydrogen atom**

Bohr model provided the expression for calculating the energy level of hydrogen atom (and hydrogen like atoms) by considering two concepts, the classical and quantum concept. The first is the classical mechanical concept that electrons revolve in circular orbit due to electrostatic force and centripetal force is equal to the Coulomb force:

Where *m _{e}* is the mass of electron, assumed to be much less than the nuclear mass. Rearranging the above equation provided the speed of electrons:

The total energy of electron at any radius is given by:

The negative total energy suggests that it require energy to take electron out of the orbit away from proton. Now according to the quantum rule, the angular momentum is an integral multiple of *nÄ§*:

*m _{e}vr *

=

*nÄ§*

Putting the value of velocity and rearranging this equation would give the value of radius of nth orbit of an atom:

For n=1 the smallest radius of hydrogen atom can be found (Z=1 for hydrogen) and its value comes out to be 5.29 Ã— 10^{-11} m. Similarly the Bohrs model enabled the calculation of energy of *nth* orbit by putting the expression of *r _{n} *in the energy expression.

Bohrs model was an important step to understand the absorption and emission spectra of atoms which contained discrete lines. Bohr model related these discrete lines in the atomic spectra to the difference in the electronic orbits in atoms. However this was not achieved by Bohr himself because the idea that the electrons can behave as material waves was suggested eleven years later but still the Bohrs concept of discrete energy levels was a significant step in understanding the electrons behavior in atom and towards the development of quantum mechanics.