Emission transitions in the Paschen series end at orbit `n = 3` and start from orbit n and can be represented as `v = 3.29 xx 10^(15) (Hz) [1//3^2 - 1//n^2]` . Calculate the value of n if the transition is observed at 1285 nm. Find the region of the spectrum.

Explanation

`v = 3.29 xx 10^(15) (1/(3^2) - 1/(n^2)) s^(-1)`
`lambda = 1285 nm`
`:. v = c/lambda = (3.0 xx 10^(8) ms^(-1))/(1285 xx 10^(-9)m)`
`= 2.33 xx 10^(14) s^(-1)`
`2.93 xx 10^(14) = 3.29 xx 10^(15) (1/9 - 1/(n^2))`
or `" " 1/9 - 1/(n^2) = (2.33 xx 10^(14))/(3.29 xx 10^(15)) = 0.0708`
`-1/(n^2) = 0.0708 - 1/9 = -0.0403`
`1/(n^2) = 0.0403`
or `" " n^2 = 24.82`
`:. n = 5`
Transition is obtained in infrared region.