Chapter 9, Problem 9.11P

(a)

Interpretation Introduction

Interpretation:

The wavelength of the radiation with frequency $\text{7}\text{.5 }\times \text{}{\text{10}}^{\text{14}}\text{ /s}$ needs to be determined. The type of radiation needs to be determined.

Concept introduction:

The wavelength and frequency of radiation are inversely related to each other as follows:

  $\text{λ = }\frac{\text{c}}{\text{υ}}$

Where

  $\begin{array}{l}\text{λ = wavelength }\\ \text{υ = frequency}\\ \text{c = speed of light = 3}\times {\text{10}}^{\text{8}}\text{ m/s}\end{array}$

The different radiations and their wavelength ranges are

Gamma radiation: ${\text{<10}}^{\text{-9}}\text{m}$

X-ray radiation: ${\text{10}}^{\text{-9}}{\text{m to10}}^{\text{-8}}\text{m}$

Ultraviolet radiation: ${\text{10}}^{\text{-8}}\text{m to 4 }\times {\text{ 10}}^{-7}\text{m}$

Visible radiation: $\text{4 }\times {\text{ 10}}^{-7}\text{m to 8 }\times {\text{ 10}}^{-7}\text{m}$

Infrared radiation: $\text{8 }\times {\text{ 10}}^{-7}{\text{m to 10}}^{-4}\text{m}$

Microwave radiation: ${\text{10}}^{-4}{\text{m to 10}}^{-1}\text{m}$

Radio waves: $>{\text{10}}^{-1}\text{m}$

Answer to Problem 9.11P

  $\text{λ = 4 }\times {\text{ 10}}^{\text{-7}}\text{m}$

UV-visible light.

Explanation of Solution

The wavelength will be calculated as

  $\text{λ = }\frac{\text{c}}{\text{υ}}$

Putting the values,

  $\text{λ = }\frac{\text{3 }\times {\text{ 10}}^8}{7.\text{5 }\times {\text{ 10}}^{14}}$

Thus,

  $\text{λ = 4 }\times {\text{ 10}}^{\text{-7}}\text{m}$

As wavelength is $\text{4 }\times {\text{10}}^{\text{-7}}\text{m}$ it could be UV-visible light.

(b)

Interpretation Introduction

Interpretation:

The wavelength of the radiation with frequency $\text{1 }\times \text{}{\text{10}}^{\text{10}}\text{ /s}$ needs to be determined. The type of radiation needs to be determined.

Concept introduction:

The wavelength and frequency of a radiation are inversely related to each other as:

  $\text{λ = }\frac{\text{c}}{\text{υ}}$

Where

  $\begin{array}{l}\text{λ = wavelength }\\ \text{υ = frequency}\\ \text{c = speed of light = 3 }\times {\text{ 10}}^{\text{8}}\text{ m/s}\end{array}$

The different radiations and their wavelength ranges are

Gamma radiation: ${\text{<10}}^{\text{-9}}\text{m}$

X-ray radiation: ${\text{10}}^{\text{-9}}{\text{m to10}}^{\text{-8}}\text{m}$

Ultraviolet radiation: ${\text{10}}^{\text{-8}}\text{m to 4 }\times {\text{ 10}}^{-7}\text{m}$

Visible radiation: $\text{4 }\times {\text{ 10}}^{-7}\text{m to 8 }\times {\text{ 10}}^{-7}\text{m}$

Infrared radiation: $\text{8 }\times {\text{ 10}}^{-7}{\text{m to 10}}^{-4}\text{m}$

Microwave radiation: ${\text{10}}^{-4}{\text{m to 10}}^{-1}\text{m}$

Radio waves: $>{\text{10}}^{-1}\text{m}$

Answer to Problem 9.11P

  $\text{λ = 3 }\times {\text{ 10}}^{\text{-2}}\text{m}$

Microwave radiation.

Explanation of Solution

The wavelength will be calculated as

  $\text{λ = }\frac{\text{c}}{\text{υ}}$

Putting the values,

  $\text{λ = }\frac{\text{3 }\times {\text{ 10}}^8}{1\times {\text{ 10}}^{10}}$

Thus,

  $\text{λ = 3 }\times {\text{ 10}}^{\text{-2}}\text{m}$

As wavelength is $\text{3 }\times {\text{ 10}}^{\text{-2}}\text{m}$ it should be microwave radiation.

(c)

Interpretation Introduction

Interpretation:

The wavelength of the radiation with frequency $\text{1}\text{.1 }\times \text{}{\text{10}}^{\text{15}}\text{ /s}$ needs to be determined. The type of radiation needs to be determined.

Concept introduction:

The wavelength and frequency of a radiation are inversely related to each other as:

  $\text{λ = }\frac{\text{c}}{\text{υ}}$

Where

  $\begin{array}{l}\text{λ = wavelength }\\ \text{υ = frequency}\\ \text{c = speed of light = 3 }\times {\text{ 10}}^{\text{8}}\text{ m/s}\end{array}$

The different radiations and their wavelength ranges are

Gamma radiation: ${\text{<10}}^{\text{-9}}\text{m}$

X-ray radiation: ${\text{10}}^{\text{-9}}{\text{m to10}}^{\text{-8}}\text{m}$

Ultraviolet radiation: ${\text{10}}^{\text{-8}}\text{m to 4 }\times {\text{ 10}}^{-7}\text{m}$

Visible radiation: $\text{4 }\times {\text{ 10}}^{-7}\text{m to 8 }\times {\text{ 10}}^{-7}\text{m}$

Infrared radiation: $\text{8 }\times {\text{ 10}}^{-7}{\text{m to 10}}^{-4}\text{m}$

Microwave radiation: ${\text{10}}^{-4}{\text{m to 10}}^{-1}\text{m}$

Radio waves: $>{\text{10}}^{-1}\text{m}$

Answer to Problem 9.11P

  $\text{λ = 2}\text{.73 }\times {\text{ 10}}^{\text{-7}}\text{m}$

Ultraviolet radiation.

Explanation of Solution

The wavelength will be calculated as

  $\text{λ = }\frac{\text{c}}{\text{υ}}$

Putting the values,

  $\text{λ = }\frac{\text{3 }\times {\text{ 10}}^8}{1.1\times {\text{ 10}}^{15}}$

Thus,

  $\text{λ = 2}\text{.73 }\times {\text{ 10}}^{\text{-7}}\text{m}$

As wavelength is $\text{2}\text{.73 }\times {\text{ 10}}^{\text{-7}}\text{m}$ it should be Ultraviolet radiation.

(d)

Interpretation Introduction

Interpretation:

The wavelength of the radiation with frequency $\text{1}\text{.5 }\times \text{}{\text{10}}^{\text{18}}\text{ /s}$ needs to be determined. The type of radiation needs to be determined.

Concept introduction:

The wavelength and frequency of a radiation are inversely related to each other as:

  $\text{λ = }\frac{\text{c}}{\text{υ}}$

Where

  $\begin{array}{l}\text{λ = wavelength }\\ \text{υ = frequency}\\ \text{c = speed of light = 3 }\times {\text{ 10}}^{\text{8}}\text{ m/s}\end{array}$

The different radiations and their wavelength ranges are

Gamma radiation: ${\text{<10}}^{\text{-9}}\text{m}$

X-ray radiation: ${\text{10}}^{\text{-9}}{\text{m to10}}^{\text{-8}}\text{m}$

Ultraviolet radiation: ${\text{10}}^{\text{-8}}\text{m to 4 }\times {\text{ 10}}^{-7}\text{m}$

Visible radiation: $\text{4 }\times {\text{ 10}}^{-7}\text{m to 8 }\times {\text{ 10}}^{-7}\text{m}$

Infrared radiation: $\text{8 }\times {\text{ 10}}^{-7}{\text{m to 10}}^{-4}\text{m}$

Microwave radiation: ${\text{10}}^{-4}{\text{m to 10}}^{-1}\text{m}$

Radio waves: $>{\text{10}}^{-1}\text{m}$

Answer to Problem 9.11P

  $\text{λ = 2 }\times {\text{ 10}}^{\text{-10}}\text{m}$

Gamma radiation.

Explanation of Solution

The wavelength will be calculated as

  $\text{λ = }\frac{\text{c}}{\text{υ}}$

Putting the values,

  $\text{λ = }\frac{\text{3 }\times {\text{ 10}}^8}{1.5\times {\text{ 10}}^{18}}$

Thus,

  $\text{λ = 2 }\times {\text{ 10}}^{\text{-10}}\text{m}$

As wavelength is $\text{2 }\times {\text{ 10}}^{\text{-10}}\text{m}$ it should be Gamma radiation.