Chapter 2, Problem 2.99CHP

Interpretation Introduction

Interpretation:

The wavelength of light emitted when the electron in $L{i}^{2+}$ falls from $n=1$ to $n=4$ has to be calculated.

Concept introduction:

Balmer-Rydberg equation:

The Balmer-Rydberg equation given by

$\begin{array}{l}\frac{\text{1}}{\text{λ}}\text{=}{\text{R}}_{\infty }\left[\frac{\text{1}}{{\text{m}}^{\text{2}}}\text{-}\frac{\text{1}}{{\text{n}}^{\text{2}}}\right]\\ \text{where,}\\ \text{λ}\text{-}\text{wavelength}\\ {\text{R}}_{\infty }\text{-}\text{Rydberg}\text{constant}\left(\text{1}\text{.097}\text{×}{\text{10}}^{\text{-2}}{\text{nm}}^{\text{-1}}\right)\\ \text{m}\text{and}\text{n}\text{-}\text{integers}\text{with}\text{n>}\text{m}\end{array}$

The wavenumber of a single-electron ions or atoms can be calculated by,

$\begin{array}{l}\frac{\text{1}}{\text{λ}}\text{=}{Z}^2{\text{R}}_{\infty }\left[\frac{\text{1}}{{\text{m}}^{\text{2}}}\text{-}\frac{\text{1}}{{\text{n}}^{\text{2}}}\right]\\ \text{where,}\\ \text{Z-}\text{Atomic }\text{number}\end{array}$