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

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.