Emission transitions in the Paschen series end at orbit `n=3` and start from orbit `n` and can be represented as `v=3.29xx10^(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

Wavelength of transition = 1285 nm
`=1285xx10^(-9)m` (Given)
`v=3.29xx10^(15)((1)/(3^(2))-(1)/(n^(2)))`
Since `v=( c)/ (lambda)`
`=(3.0xx10^(8) ms^(-1))/(1285xx10^(-9)m)`
Now,
`v=2.33xx10^(14)s^(-1)`
Substituting the value of V in the given expression,
`3.29xx10^(15)((1)/(9)-(1)/(n^(2)))=2.33xx10^(14)`
`(1)/(9)-(1)/(n^(2))=(2.33xx10^(14))/(3.29xx10^(15))`
`(1)/(9)-0.7082xx10^(-1)=(1)/(n^(2))`
`implies (1)/(n^(2))=1.1xx10^(-1)-0.7082xx10^(-1)`
`(1)/(n^(2))=4.029xx10^(-2)`
`n=sqrt((1)/(4.029xx10^(-2)))`
`n=4.98 n`
`~~5`
Hence, for the transition to be observed at 1285 nm, n = 5.
The spectrum lies in the infra-red region.