Chapter 11.1, Problem 7RQ

Interpretation Introduction

Interpretation: The energy of 10⁴ m radio waves is to be calculated.

Concept Introduction: The energy of a wave can be calculated using Planck’s relation.

Answer to Problem 7RQ

The energy of radio waves was found to be 1.198 kJ/mol.

Explanation of Solution

  $\begin{array}{l}{\text{Wavelength of AM wave=1×10}}^{\text{4}}\text{ m}\hfill \\ {\text{Speed of electromagnetic wave c=3×10}}^{\text{8}}{\text{ ms}}^{\text{-1}}\hfill \\ \begin{array}{l}\text{Energy of wave }E=\frac{hc}{\lambda }\\ E\text{=}\frac{\text{6}{\text{.63×10}}^{\text{-34}}{\text{×3×10}}^{\text{8}}}{{\text{1×10}}^{\text{4}}}\\ E\text{=1}{\text{.989×10}}^{\text{-21}}\text{ J}\end{array}\hfill \end{array}$

This is the energy of one wave.

Energy of 1 mol waves,

  $\begin{array}{c}{E}_{mol}\text{=}E\times n_A\\ E_{mol}\text{=1}{\text{.989×10}}^{\text{-21}}\text{×6}{\text{.022×10}}^{\text{23}}\\ E_{mol}\text{=1}{\text{.198×10}}^{\text{3}}\text{ J/mol}\\ \text{=1}\text{.198 kJ/mol}\end{array}$