Question

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

Answer 1

First, calculate the frequency from the wavelength.

$\nu =\frac{c}{\lambda }=\frac{3.0\times {10}^8}{1285\times {10}^{-9}}=2.33\times {10}^{14}/s$ ......(1)

But as given, $\nu =3.29\times {10}^{15}\left(Hz\right)[\frac{1}{3^2}-\frac{1}{n^2}]$ ......(2)

From (1) and (2),

$2.33\times {10}^{14}=3.29\times {10}^{15}\left(Hz\right)[\frac{1}{3^2}-\frac{1}{n^2}]$

$n=5$

The transition belongs to the infrared region.