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Structure Of Atom

Question
CBSEENCH11005299

How will you correlate Bohr’s concept of hydrogen atom with de-Broglie concept?
Or
Show that the circumference of Bohr orbit for the hydrogen atom is an integral multiple of de-Broglie wavelength associated with electron revolving around the orbit.

Solution
According to Bohr’s theory,
   space space space space space space space space space space space space space space space space space space space mvr space equals space straight n fraction numerator straight h over denominator 2 straight pi end fraction space space where space straight n space equals space 1 comma space 2 comma space 3.....
space space space space space space or space space space space space 2 πr space equals space straight n fraction numerator straight h over denominator 2 straight pi end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis
According to de-Broglie equation,
       
              space space space space space space space space space space straight lambda space equals space fraction numerator straight h over denominator m v end fraction                   ...(2)
From equations (1) and (2), we have
              space space space 2 πr space equals space nλ                                ...(3)
From eq. (3), it is evident that circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de-Broglie wavelength.