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Bohr’s Correspondence Principle

Hello friends!  Welcome again on our blog today I’m going to discuss Bohr’s correspondence principle. In my last post I’ve discussed Discovery of Heavy Hydrogen. If you haven’t read this post you can go through above link..
Okk let us start…. 

The quantum theory give results which are all together different from results given by classical mechanics. 
According to Classical theory, an electron moving in circular orbit must emit radiations only of a particular frequency. 
On the other hand, according to Quantum theory, radiation is emitted when electrons jumps from higher orbit to lower orbit. 

To corelate these theories, Bohrs in 1923, enunciated a principle which established a correspondence between the classical frequency and the quantum frequency. This principle consists of two parts :

i) The predictions of quantum theory for behavior of any physical system must coincides with the predictions of classical theory. 

ii) Any selection rule which are necessary to obtain the required correspondence in the limit of large quantum numbers also hold for small quantum numbers.

Let us apply this principle to Hydrogen atom. Let “v” be the velocity of electron ( mass “m”, charge “e”) revolving in Bohr orbit of radius “r” of hydrogen atom. For mechanical stability of electron :

      Centripital Force = Electrostatic Force 

Now, we’ve to find time period & frequency in this case which can be done as :

where, “f” is frequency which must be radiated by moving electron classically. 

The energy of electron in nth orbit according to quantum mechanics is :

i.e. “for every large number ‘n’ ,the quantum frequency  Ï… of radiation is identical with classical frequency ‘f’ of the revolution of the electron.”

This is Bohr’s Correspondence principle. 
I hope you understand this topic. In my next tutorial I’ll explain other important topics of Atomic Physics. 
Want to ask any questions ?? Ask us in comment box, we’ll answer as soon as possible! 
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