Question
Tue March 03, 2015 By: Mahesh010167

how that de Broglie hypothesis of matter waves is in agreement with Bohr's theory.

 

Expert Reply
Jyothi Nair
Wed March 04, 2015
The de-Broglie hypothesis of matter wave supports the Bohr's concept of stationary orbit. 
According to de-Broglie hypothesis, a wave is associated with moving material particle which controls the particle in all aspects.This wave associated with moving particle is called matter wave whose wavelength is called de-Broglie wavelength.The wavelength λ of the wave associated with electron while moving with velocity v is given by:
begin mathsize 14px style straight lambda equals straight h over mv end style ---------(1)
where h is the planck's constant and m the mass of the particle.
According to this hypothesis, a stationary orbit is that orbit whose circumference is integral mutiple of wavelength of wave associated with electron in that orbit.
Let λ be the de-Broglie wavelength of electron while revolving in nth orbit of radius r, then we can write it as:

begin mathsize 14px style 2 πr space equals space nλ straight lambda space equals space fraction numerator 2 πr over denominator straight n end fraction space space space minus negative negative negative negative negative negative negative negative left parenthesis 1 right parenthesis From space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis space we space can space write colon fraction numerator 2 πr over denominator straight n end fraction equals straight h over mv mvr space equals space straight n open parentheses fraction numerator straight h over denominator 2 straight pi end fraction close parentheses straight i. straight e space Total space angular space momentum space equals space straight n open parentheses fraction numerator straight h over denominator 2 straight pi end fraction close parentheses end style
This is as stated by Bohr's postulate about stable orbits.
i.e. Electrons revolve only in stationary orbits for which total angular momentum of the revoving electron is an integral mutiple of h/2π 
i.e. mvr =n(h/2π)
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