Chapter 8, Problem 8A.1E

Interpretation Introduction

Interpretation:

The wavenumber and wavelength of the given line in Balmer series has to be calculated.

Concept-Introduction:

In 1885, Johann Balmer developed a simple equation which could be used to calculate the wavelengths of the four visible lines in the emission spectrum of hydrogen. Johannes Rydberg developed Balmer’s equation further, giving an equation which could calculate the visible wavelengths and also those of all hydrogen’s spectral lines.

  $\frac{\text{1}}{\text{λ}}={\text{ R}}_{\infty }\left(\frac{\text{1}}{{\text{n}}_{\text{1}}{}^{\text{2}}}-\frac{\text{1}}{{\text{n}}_{\text{2}}{}^{\text{2}}}\right)$

This equation is known as the Rydberg equation. Here, $\text{λ}$ is the wavelength of a line in the spectrum; ${\text{R}}_{\infty }$ is the Rydberg constant ($\text{1}{\text{.09737316 × 10}}^{\text{7}}{\text{ m}}^{-1}$ for $\text{H}$ atom); and ${\text{n}}_{\text{1}}{\text{ and n}}_{\text{2}}$ are positive integers, where ${\text{n}}_{\text{2}}{\text{ > n}}_{\text{1}}$.