By referring to Balmer Formula:

We know that

Wave Number

For Balmer series, the values of n₁ = 2 and the value of R_h = 109678

Wave number is inversely proportional to the wavelength of light. So for light of long wavelength, wave number has to be minimum. For minimum condition the value of n₂ should be equal to 3.

Wave Number

= [109678×5] / 36

= 548390 / 36

= 15233.0556 cm^-1

Therefore, the wave number for longest wavelength is 15.233× 10³ cm^-1.