Derive an expression for the frequency of spectral series by assuming the expression for the total energy of the election of hydrogen.

Explanation

Suppose an electron jumps from `n^(th)` higher orbit to `p^(th)` lower orbit.
Let `E_(n) and E_(p)` be the energies of electron in `n^(th) and p^(th)` orbit respectively.
`:.` Energy of electron in `n^(th)` orbit is,
`E_(n)=-((me^(4))/(8 epsi_(0)^(2)h^(2)))*(1)/(p^(2)) " "...(i)`
Energy of electron in `p^(th)` orbits is,
`E_(p)=-((me^(4))/(8 epsi_(0)^(2)h^(2)))*(1)/(p^(2)) " "...(ii)`
According to Bohr's `3^(rd)` postulate,
`:.` Energy, Emitted,
`hv=E_(n)-E_(p)`
`hv=(me^(4))/(8 epsi_(0)^(2)h^(2))*((1)/(p^(2))-(1)/(n^(2)))`
`v=(me^(4))/(8 epsi_(0)^(2)h^(3))*((1)/(p^(2))-(1)/(n^(2)))`
`:. (1)/(lambda)=(me^(4))/(8 epsi_(0)^(2)h^(3)c)*((1)/(p^(2))-(1)/(n^(2))) ( :. v=(c)/(lambda))`
`(1)/(lambda)=R((1)/(p^(2))-(1)/(n^(2)))`
where `R=(me^(4))/(8epsi_(0)^(2)h^(3)c)` is called Rydberg's constant.
This relation is called Bohar's formula for hydrogen Spectral line.