Chapter 5, Problem 45A

Interpretation Introduction

(a)

Interpretation:

From the figure radiation type with a frequency of $8.6\times {10}^{11}{\text{s}}^{-1}$ needs to be explained.

Concept introduction:

All types of electromagnetic radiation are included in electromagnetic spectrum. All types of radiation are different in their frequencies and wavelength values.

Answer to Problem 45A

The type of radiation is infrared.

Explanation of Solution

From the given figure, it is clear that frequency of $8.6\times {10}^{11}{\text{s}}^{-1}$ falls between the range of infrared. Hence, the radiation type is infrared.

Interpretation Introduction

(b)

Interpretation:

From the figure radiation type with wave length 4.2 nm needs to be explained.

Concept introduction:

All types of electromagnetic radiation are included in electromagnetic spectrum. All types of radiation are different in their frequencies and wavelength values.

Answer to Problem 45A

The type of radiation is x-ray.

Explanation of Solution

The speed of an electromagnetic wave is expressed by below formula:

$\begin{array}{l}\text{Speed}=\text{wavelength}\times \text{frequency}\\ \text{frequency}=\frac{\text{Speed}}{\text{wavelength}}\end{array}$ …… (1)

Convert nanometer into meter as follows:

$\begin{array}{c}1\text{nm}={10}^{-9}\text{m}\\ 4.2\text{nm}=\frac{4.2\text{nm}\times {10}^{-9}\text{m}}{1\text{nm}}\\ =4.2\times {10}^{-9}\text{m}\end{array}$

The value of speed is $3\times {10}^8\text{m}/\text{s}$.

Substitute above values in equation (1).

$\begin{array}{c}\text{frequency}=\frac{\text{Speed}}{\text{wavelength}}\\ =\frac{3\times {10}^8\text{m}/\text{s}}{4.2\times {10}^{-9}\text{m}}\\ =0.714\times {10}^{8+9}{\text{s}}^{-1}\\ =7.14\times {10}^{16}{\text{s}}^{-1}\end{array}$

Hence, frequency is $7.14\times {10}^{16}{\text{s}}^{-1}$.

From the diagram the frequency value is in the range of x-rays.

Interpretation Introduction

(c)

Interpretation:

From the figure radiation type with a frequency of $5.6\text{MHz}$ needs to be explained.

Concept introduction:

All types of electromagnetic radiation are included in electromagnetic spectrum. All types of radiation are different in their frequencies and wavelength values.

Answer to Problem 45A

The type of radiation is AM radio.

Explanation of Solution

Convert MHz into Hz as follows:

$\begin{array}{c}1\text{MHz}={10}^6\text{Hz}\\ 5.6\text{MHz}=\frac{5.6\text{MHz}\times {\text{10}}^6\text{Hz}}{1\text{MHz}}\\ =5.6\times {\text{10}}^6\text{Hz}\end{array}$

$5.6\text{MHz}$ is equivalent to $5.6\times {\text{10}}^6\text{Hz}$. From the given figure, it is clear that frequency of $5.6\times {\text{10}}^6\text{Hz}$ falls between the range of radio.

Interpretation Introduction

(d)

Interpretation:

From the figure radiation that travels at a speed of $3.00\times {10}^8\text{m}/\text{s}$ is needs to be explained.

Concept introduction:

All types of electromagnetic radiation are included in electromagnetic spectrum. All types of radiation are different in their frequencies and wavelength values.

Answer to Problem 45A

All type of radiation passes through the speed $3.00\times {10}^8\text{m}/\text{s}$.

Explanation of Solution

The speed of all type of radiation is $3.00\times {10}^8\text{m}/\text{s}$. Hence, the radiation of any type has the speed of $3.00\times {10}^8\text{m}/\text{s}$.