The shortest and the longest wavelength in the Balmer series of the hydrogen spectrum are? Rydberg constant, RH = 109678 cm-1

By BYJU'S Exam Prep

Updated on: September 25th, 2023

(a) 911.7 Å and 1215.7 Å

(b) 3647 Å and 6565 Å

(d) 911.7 Å and 6565 Å

The shortest and the longest wavelength in the Balmer series of the hydrogen spectrum are 3647 Å and 6565 Å. We know that for the Balmer series, n1 = 2

The energy difference between the two states exhibiting the transition should be at its maximum for the shortest wavelength in the Balmer series (also known as the series limit).

n2 = ∞

So 1/λ = RH [1/22 – 1/∞2] = RH/4

Substituting the values we get:

λ = 4/109678 = 3.647 x 10-5 cm

In simplification we get the:

= 3647 Å

Table of content

1. The shortest and the longest wavelength in the Balmer series of the hydrogen spectrum are? Rydberg constant, RH = 109678 cm-1

The energy difference between the states showing the transition should be at its smallest for the longest wavelength in the Balmer series (i.e., the first line), i.e. n2 = 3

1/λ = RH [1/22 – 1/32] = 5/36RH

Substituting the values we get:

λ = 36/5 x 1/RH = 36/ (5 x 109678) = 6.565 x 10-5 cm

In simplification we get the:

= 6565 Å

Hydrogen Spectrum

A key piece of evidence for the quantized electronic structure of an atom is the hydrogen spectrum. As soon as an electric discharge passes through a gaseous hydrogen molecule, the molecule’s hydrogen atoms disintegrate.
The energetically excited hydrogen atoms cause the emission of electromagnetic radiation, which is what happens.
The hydrogen emission spectrum includes distinct frequency radiation. These radiation series bear the names of the researchers who first identified them.

Summary: