Textbook Problem

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Cellular phones operate at frequencies of approximately 850 megahertz. What is the wavelength of the radio waves used by cell phones?

Interpretation Introduction

Interpretation:

The wavelength of radio waves used by cell phones is to be calculated.

Concept Introduction:

The electromagnetic spectrum is the range of all types of radiation.

Electromagnetic waves are described by three properties, namely, frequency $\text{(ν)}$, wavelength $\text{(λ)}$ and energy of the photon (E) which are related to each other by the following formula:

$\begin{array}{c}E=\left(\frac{\text{h}\times \text{c}}{\lambda }\right)\\ =\text{h}\times \nu \end{array}$

Here “$\text{h}$” is Plank’s constant, “$\lambda$” is the wavelength, “$\nu$” is the frequency and “$\text{c}$” is the speed of light.

Radio waves are a form of electromagnetic radiation with long wavelengths. The energy of radio waves is quite small. The radio captures radio waves emitted by the radio stations.

Explanation of Solution

Given information: The frequency of radio waves is $850$ megahertz.

The energy of the photons is given by the following expression:

$\begin{array}{c}E=\frac{\text{hc}}{\lambda }\\ =\text{h}\nu \end{array}$

Here,

$\text{h}=6.626\times {10}^{-34}\text{J s (planks constant), c}=3\times {10}^8\text{m/s (speed of light) and }\lambda \text{ is wavelength of radiation}$

Also, $$