What is the shortest wavelength present in the Paschen series of spectral lines?

Explanation

From Rydberg.s formula , we have
`1/lambda=R[1/n_1^2-1/n_2^2]`
where R=Rydberg.s constant =`1.097xx10^7 m^(-1)`
`n_f`=final energy level
`n_i` = initial energy level
For smallest wavelength of Paschen series , `n_f`=3 and `n_i=oo`
`therefore 1/lambda=R[1/3^2-1/oo]=R/9`
`rArr lambda=9/R =9/(1.097xx10^7)`
`=8.2xx10^(-7)`m = 820 nm