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.

A particle of chagre equal to that of anelectron and mass 208 times th

1.	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» Solution :Centrifgal force =Electrostaticforce (a) `(1)/(4lambdaepsilon_(0)).(3e.e)/(r^(2))=(208me.(V^(2))/(r))"".......(i)` `mvr=(nh)/(2pi)""....(2)` `r=(208)/(3e^(2)).(4piepsilon_(0))(v^(2)r^(2))` `=(N^(2)h^(2))/(k.4pi^(2).3e^(2).208me)` (b) `r=r_(0).n^(2)=6.9xx106n^(2)=0.53xx10^(-10)m` `n^(2)~~625` `n=25` (c)`DELTAE=(1)/(2)m(V_(3)^(2)-V_(1)^(2))=(HC)/(lambda)` putting the value of`V_(3)` and `V_(1)` from eq.(1) and (2) `lambda=55.2xx10^(-12)m`