2.55 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.

The wavelength of transition = 1285 nm
= 1285 × 10–9 m (Given)

v = 3.29 x 1015 132 - 1n2

Since v = cλ
= 3.0 x 108 m/s1285 x 10-9 m
Now,
v = 2.33 x 1014 s-1
Substituting the value of ν in the given expression, 
3.29 x 101519 - 1n2 = 2.33 x 1014
19 - 1n2 = 2.33 x 10143.29 x 1015
19 - 0.7082 x 10-1 = 1n2
 1n2 = 1.1 x 10-1 -0.7082 x 10-1
1n2 = 4.029 x 10-2
n = 14.029 x 10-2
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.