A particle of chagre equal to that of an electron 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 applicable to this system ,(a) dervie am expression for the radius of the radius of the nth bohar orbit ,(b) find the value of n for which the radius wavelenght of the raditatio emitted when the revolving particle jumps from the thrid orbit to the first.

A particle of chagre equal to that of an electron and mass 208 times t

1.	A particle of chagre equal to that of an electron 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 applicable to this system ,(a) dervie am expression for the radius of the radius of the nth bohar orbit ,(b) find the value of n for which the radius wavelenght of the raditatio emitted when the revolving particle jumps from the thrid orbit to the first.
Answer» Correct Answer - `r_(n)=(n^(2)h^(2))/(4Kpi^(2)xx3e^(2)xx208m_(e))n=25;55.2` pm Centrifgal force =Electrostatic force (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`

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