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

Explanation

By formula of wavelength of spectral line,
`(1)/(lambda_(if))=R[(1)/(n_(f)^(2))-(1)/(n_(i)^(2))]`
For Paschen series `n_(f) = 3` and for shorte wavelength `n_(i)=oo`
`:.lambda_(min)=R[(1)/(3^(2))-(1)/(oo^(2))]`
`:. lambda_(min)=1.097xx10^(7)xx[(1)/(9)] " " [ :. (1)/(oo^(2))=0]`
`:. lambda_(min)=(9)/(1.097xx10^(7))`
`:. lambda_(min)=8.20419xx10^(-7)m`
`:. lambda_(min)=820xx10^(-9)m`
`:. lambda_(min)=820.54 nm=820 nm`