Establish the radiation formula
`bar v = R [ 1/n_1^2 - 1/(n_2^2)] [ "Take"E_n = (-mq^4)/(8 epsi_0^2 n^2 h^2)]`
State the transition rule of Paschen series.

Explanation

According to Bohr.s theory,
`DeltaE = h_1v = E_2 - E_1` …(i)
When `n = n_1 , E_1 = -(MZ^2 e^4)/(8 epsi_0^2 n_1^2 h^2)`
When `n = n_2, E-2 = - (MZ^2 e^4)/(8 epsi_0^2n_2^2 h^2)`
`:.hv = (mZ^2 e^4)/(8 epsi_0^2 h^2) (1/n_1^2 - 1/n_2^2) ["from Eq. (i)"]`
`rArr (hc)/lambda = (mZ^2 e^4)/(8 epsi_0^2 h^2) (1/n_1^2 - 1/n_2^2)`
`rArr 1/lambda = barv = (mZ^2 e^4)/(8 epsi_0^2 h^3 C) (1/n_1^2 - 1/n_2^2)`
` = R (1/n_1^2 - 1/n_2^2)`
where, `R = (mZ^2 e^4)/(8 epsi_0^2 h^3 C) =` constant.
For paschen series,
`1/lambda = barv = R (1/3^2 - 1/n^2 ), n =4,5,6`...
It lies in infrared region.