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The given frequency of the emission transition in the Paschen series

\[v=3.29X{{10}^{15}}(Hz)[1/{{3}^{2}}-1/{{n}^{2}}].\] -- (1)

And also, frequency $v=\dfrac{c}{\lambda }=\dfrac{3X{{10}^{8}}m/s}{1285X{{10}^{-9}}m}$ --- (2)

Where, the transition observed = 1285nm, c= velocity of light

From equation (1) and (2), the both equations represent the frequency, then both values will resemble equal values.

Equation (1) = equation (2)

\[v=3.29X{{10}^{15}}(Hz)[1/{{3}^{2}}-1/{{n}^{2}}]\]

= $\dfrac{3X{{10}^{8}}}{1285X{{10}^{-9}}}$

Therefore, $\dfrac{1}{{{n}^{2}}}=\dfrac{1}{9}-\dfrac{3X{{10}^{8}}}{1285X{{10}^{-9}}}X\dfrac{1}{3.29X{{10}^{15}}}$ = 0.111-0.071=0.04

Hence, $\dfrac{1}{{{n}^{2}}}=\dfrac{1}{25}\Rightarrow n=5$

So, the value of the transition which is observed at 1285nm is n=5

The radiation corresponding to infrared region is 700nm to millimeter (mm)

The value of the transition n=5 is 1285nm in the infrared region.

Finally the region observed for the given transition is the infrared region.