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A particle of chagre equal to that of anelectron and mass 208 times the mass of the electron moves in a circular orbit around nucleus of chagre +3e. Assuming that the Bohar of the atom is applicableto this system ,(a) dervie am expression for the radius of the radius of the nth boharorbit ,(b) find the value of n for which the radius wavelenght of the raditatio emitted when the revolvingparticle jumps from the thrid orbit to the first.

Answer» <html><body><p><br/></p>Solution :Centrifgal force =Electrostaticforce<br/>(a) `(1)/(4lambdaepsilon_(0)).(3e.e)/(r^(2))=(208me.(V^(2))/(r))"".......(i)` <br/> `mvr=(nh)/(2pi)""....(2)`<br/> `r=(<a href="https://interviewquestions.tuteehub.com/tag/208-292892" style="font-weight:bold;" target="_blank" title="Click to know more about 208">208</a>)/(3e^(2)).(4piepsilon_(0))(v^(2)r^(2))`<br/> `=(<a href="https://interviewquestions.tuteehub.com/tag/n-568463" style="font-weight:bold;" target="_blank" title="Click to know more about N">N</a>^(2)h^(2))/(k.4pi^(2).3e^(2).208me)`<br/> (b) `r=r_(0).n^(2)=6.9xx106n^(2)=0.53xx10^(-<a href="https://interviewquestions.tuteehub.com/tag/10-261113" style="font-weight:bold;" target="_blank" title="Click to know more about 10">10</a>)m` <br/> `n^(2)~~625`<br/>`n=25`<br/>(c)`<a href="https://interviewquestions.tuteehub.com/tag/deltae-2053238" style="font-weight:bold;" target="_blank" title="Click to know more about DELTAE">DELTAE</a>=(1)/(2)m(V_(3)^(2)-V_(1)^(2))=(<a href="https://interviewquestions.tuteehub.com/tag/hc-1016346" style="font-weight:bold;" target="_blank" title="Click to know more about HC">HC</a>)/(lambda)` <br/> putting the value of`V_(3)` and `V_(1)` from eq.(1) and (2) `lambda=55.2xx10^(-12)m`</body></html>


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