A particle of charge equal to that of an electron and mass `208` times the mass of the electron moves in a circular orbit around a nucleus of charge `+3e`. Assuming that the Bohr model of the atom is applicable to this system, (a) derive an expression for the radius of the `n^(th)` bohr orbit, (b) find the value of n for which the radius of the orbit is approximately the same as that of the first Bohr orbit for the hydrogen atom, and (c ) find the wavelength of the radiation emitted when the revolving particle jumps from the third orbit to the first.

A particle of charge equal to that of an electron and mass `208` times

1.	A particle of charge equal to that of an electron and mass `208` times the mass of the electron moves in a circular orbit around a nucleus of charge `+3e`. Assuming that the Bohr model of the atom is applicable to this system, (a) derive an expression for the radius of the `n^(th)` bohr orbit, (b) find the value of n for which the radius of the orbit is approximately the same as that of the first Bohr orbit for the hydrogen atom, and (c ) find the wavelength of the radiation emitted when the revolving particle jumps from the third orbit to the first.
Answer» Correct Answer - `r_(n)=(n^(2)h^(2))/(4Kpi^(2)xx3e^(2)xx208m_(e));n=25 ; 55.2 "pm"` (a) `(1)/(lambda)=((1)/(lambda_(1))+(1)/(lambda_(2)))=rxx4[(1)/(1^(2))-(1)/(n^(2))]` (b) `DeltaE_(2rarr4)=2.7=IE[(1)/(4)-(1)/(16)]` `IE=2.7xx(16)/(3)eV` (c ) `Deltaoverset("max")E_(4rarr1)=IE[(1)/(k)-(1)/(1)]` `DeltaE_(4rarr3)=IE[(1)/(16)-(1)/(9)]`

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