Chapter 7, Problem 7.13P

Interpretation Introduction

Interpretation:

The wavelength of $22.235\text{ GHz}$ frequency microwave radiation in nanometers, and angstroms is to be determined.

Concept introduction:

Electromagnetic waves are radiations that are formed by oscillating electric and magnetic fields. The electric and magnetic field components of an electromagnetic wave are perpendicular to each other.

Energy is proportional to the frequency and is expressed by the Plank-Einstein equation as follows:

$E=h\nu$

Here,

$E$ is the energy.

$h$ is the Plank’s constant.

$\nu$ is the frequency.

The equation to relate the frequency and wavelength of electromagnetic radiation is as follows:

$\nu =\frac{c}{\lambda }$

Here,

$c$ is the speed of light.

$\lambda$ is the wavelength.

Rearrange the above equation for $\lambda$.

$\lambda =\frac{c}{\nu }$ (1)

The conversion factor to convert frequency from $\text{ GHz}$ to $\text{Hz}$ is,

$1\text{ GHz}={10}^9\text{ Hz}$

The conversion factor to convert frequency from $\text{Hz}$ to ${\text{s}}^{-1}$ is,

$1\text{ Hz}=1{\text{ s}}^{-1}$

The conversion factor to convert wavelength from $\text{nm}$ to $\text{m}$ is,

$1\text{ nm}=1\times {10}^{-9}\text{ m}$

The conversion factor to convert wavelength from $\stackrel{\text{o}}{\text{A}}$ to $\text{m}$ is,

$1\stackrel{\text{o}}{\text{A}}=1\times {10}^{-10}\text{ m}$