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In 1913, Bohr’s satisfactorily defined the atomic model. He made following assumptions /postulates :-







1). Bohr’s First Postulate :-

The electrons rotate around the nucleus in various stationary & non radiating circular orbit.

The necessary centripetal force to keep the electrons in closed circular orbit is provided by electrostatic attractions between electron & nucleus.

If “m” be the mass of electron ,”v” the velocity of electron in circular orbit & “r” be its radius.


Then Centripetal force = mv2/R


If Z is atomic number of atom, then charge on nucleus  = Ze


The Coulomb force between nucleus & electron :










According to Bohr’s ,




Centripetal force = Coulomb force







2). Bohr’s IInd postulate :-

Only those orbits are permissible for electrons in which the total angular momentum of electron is equal to an integral multiple of h/2π ,where h is Plank’s constant.

n is called principle quantum number. 

This equation is called Bohr’s quantum condition.

3). Bohr’s IIIrd postulate :-


No energy is radiated by the atom so long as the electron continues to move in its stationary orbit.

The emission or absorption of energy takes place only when an electron jumps from one permitted orbit to another.

If E1 and E2 are energies of two states (orbits), then the frequency  ν of radiation emitted or absorbed is given by :



            


This is known as Bohr’s (or Einstein) frequency condition.


With these postulates Bohr was able to explain the observations made by Balmer, Paschen and others.


i.e. the radii of permitted orbits are in ratio 1:4:9:16:……
Subsituting the value of r in equation (v) 

  










From this, it is clear that the velocity of an electron decreases with increase in order of the orbit.

Energy of Electron:










Also ,the potential energy is given by :


“the work done in bringing the electrons of charge e from infinity to a distance “r” from nucleus of charge  “Ze”.


which gives the energy of electron revolving in thenth orbit. 

When an electron jumps from outer orbit into the inner orbit. The difference in energies of two orbits is emitted as light of frequency   ν  given by :-









For Hydrogen atom:-









The wave number corresponding to these frequencis is given by :


              











   This is Bohr’s theory of hydrogen spectrum & energy of electron on basis of it. I hope you understand this derivation, still any query you can always write to us in comment section. Thanks for your patience to read full article. 😊