For atomic hydrogen, the Paschen series of lines occurs when nf = 3, whereas the Brackett series occurs when nf = 4 in the equation 1 λ = 2π2mk2e4 h3c (Z2) 1 n2f − 1 n2i . Using this equation, show that the ranges of wavelengths in these two series overlap.

So the two wavelength range will over lap

Explanation:

The Rydberg equation is given by

m is the mass of electron

k = 1/4π∈₀

∈₀ = is the permitivity of free space

e is the charge of electron

h is the plank constant

c is the speed of light in vaccum

z is the atomic number = 1

where R is the  Rydberg constant = 1.097373 × 10⁷m⁻¹

For  Paschen series of H spectrum

in Paschen series of H spectrum

The maximum wavelength occur for

The minimum wavelength occur for = ∞

The brackett series of H spectrum

The maximum wavelength occur for

The minimum wavelength occur for = ∞

So the two wavelength range will over lap