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CBSE Class 12-science Answered

using bohrs famous quantisation condition for angular momentum show that the circumference of nelectron in the nth orbital state in hydrogen atom is n times the de broglie wavelength associated with it. the electron in hydrogen atom is initially in 3rd excited state .what is the maximum no of spectral line emitted when it finally comes to ground state?
Asked by vasturushi | 28 Feb, 2018, 02:12: AM
answered-by-expert Expert Answer
Bohr's second postulate of quantisation says that the allowed values of angular momentum are integral multiples of h/2π.
 
Hence begin mathsize 12px style L subscript n equals space m v subscript n r subscript n space equals space fraction numerator n h over denominator 2 pi end fraction end style
Above equation that express the condition for angular momentum quantaisation is rewritten as below
 
begin mathsize 12px style 2 pi space r subscript n space equals space n fraction numerator h over denominator m v subscript n end fraction semicolon i n space t h e space a b o v e space e q u a t i o n comma space L H S space i s space c i r c u m f r e n c e space o f space n to the power of t h end exponent space o r b i t space a n d space fraction numerator h over denominator m v subscript n end fraction space i s space d e B r o g l i space w a v e l e n g t h. end style
Hence the first part of question is proved.
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3rd excited state n =4; hence three transitions are possible (i) n=4 to n=1 (Lyman series), (ii) n=4 to n=2 (Balmer series) , (iii) n=4 to n=3 (Paschen series)
Answered by Thiyagarajan K | 28 Feb, 2018, 02:09: PM

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