The ratio of the longest wavelength to the shortest wavelength in Paschen series of hydrogen spectrum is:

Question

Question

This question was previously asked in

AAI ATC Junior Executive 27 July 2022 Shift 1 Official Paper

Answer 1

Concept:

Hydrogen spectrum:

The hydrogen spectrum is an important piece of evidence to show the quantized electronic structure of an atom.
The hydrogen atoms of the molecule dissociate as soon as an electric discharge is passed through a gaseous hydrogen molecule.
It results in the emission of electromagnetic radiation initiated by the energetically excited hydrogen atoms.
The hydrogen emission spectrum comprises radiation of discrete frequencies.

First three spectral series in the hydrogen spectrum: Lyman, Balmer, and Paschen series
The formula for the wavelength, where, p = higher energy level, n = lowest energy level, λ = wavelength
Here R = 109677 is called the Rydberg constant for the hydrogen atom

Calculation:

The longest wavelength in the Paschen series was obtained when p = 3, n = 4

For the longest wavelength,

The shortest wavelength in the Paschen series was obtained when p = 3, n = ∞

For the shortest wavelength,

Ratio,