An imaginary particle has a charge equal to that of an electron and mass 100 times the mass of the electron. It moves in a circular orbit around a nucleus of charge + `4 e`. Take the mass of the nucleus to be infinite. Assuming that the Bhor model is applicable to this system. (a)Derive an expression for the radius of `n^(th)` Bhor orbit. (b) Find the wavelength of the radiation emitted when the particle jumps from fourth orbit to the second orbit.

Answer

(i) `(n^(2)h^(2)epsi_(0))/(400pime^(2))` (ii) `408 eV`

Explanation

(i) `mvr_(n)=(nh)/(2pi)` and `(mv^(2))/r_(n)=(4e^(2))/(4pi in_(0) r_(n)^(2))`
`implies r_(n)=(in_(0) h^(2))/(4pi e^(2))(n^(2)/m)=(n^(2)h^(2)in_(0))/(400 pi me^(2))`
(iii) `E_(n^(th))=-(13.6) ((Z^(2)m)/n^(2))`
`DeltaE=13.6xx4^(2)xx100 [1/2^(2)-1/4^(2)]=408 eV`