The force of repulsion between two electrons kept at a distance of 1 m is F. if m is the mass of the electron, h is the planck's constant and c is the velocity of light, then the Rydberg's constant of

Options

A. `(F^(2)2pi^(2)m)/(h^(3)c)`
B. `(F2pi^(2)m)/(h^(3)c)`
C. `(h^(3)c)/(F^(3)2pi^(2)m)`
D. `(F2pi^(2)m)/(h^(2)c)`

Answer

A

Explanation

Rydberg's constant can be written as
`R=(me^(4))/(8epsi_(0)^(2)Ch^(3))`
also, `F=(1)/(4piepsi_(0))(e^(2))/((1)^(2))`
`becauser=1`
`thereforeF^(2)=(e^(4))/(16pi^(2)epsi_(0)^(2))`
From the given options (a) is the correct option as
`therefore(F^(2).2pi^(2)m)/(Ch^(3))=(e^(4))/(16pi^(2)epsi_(0)^(2))xx(2pi^(2)m)/(Ch^(3))`
`=(me^(4))/(8epsi_(0)^(2)Ch^(3))=R`