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 t

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» Solution :(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)]`