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Question:

Emission transitions in the Paschen series end at orbit n = 3 and start from orbit n and can be represented as v=3.29×10¹⁵(Hz)[1/3²−1/n²]. Calculate the value of n if the transition is observed at 1285 nm. Find the region of the spectrum.

Solution:

First, calculate the frequency from the wavelength.
ν=c/λ=3.0×10⁸/1285×10⁻⁹=2.33×10¹⁴/s. (1)
But as given,
ν=3.29×10¹⁵(Hz)[1/3²−1/n²]. (2)
From (1) and (2),
2.33×10¹⁴=3.29×10¹⁵(Hz)[1/3²−1/n²]
n=5
The transition belongs to the infrared region.