Chapter 7, Problem 7.14P

(a)

Interpretation Introduction

Interpretation:

The frequency of the IR radiation of wavelength $9.6\text{ μm}$ 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:

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

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

$1\text{ μm}=1\times {10}^{-6}\text{ m}$

(b)

Interpretation Introduction

Interpretation:

The wavelength of the IR radiation of frequency $8.652\times {10}^{13}\text{ Hz}$ 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:

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

Rearrange the above equation for $\lambda$.

$\lambda =\frac{c}{\nu }$ (2)