Chapter 2, Problem 17Q

(a)

Interpretation Introduction

Interpretation:

The region of the electromagnetic spectrum for the given wavelength has to be specified.

Concept-Introduction:

Wavelength: The distance between successive peaks in a wave and measured in units of length.

Frequency: The number of waves passed a point in a certain amount of time.

Relation between wavelength and frequency:

$\text{Frequency}\left(\text{ν}\right)\text{=}\frac{\text{speed}\text{of}\text{light}\left(\text{c}\right)}{\text{wavelength}\left(\text{λ}\right)}$

Where, c is constant, the value of c is $\left(\text{3}{\text{.00×10}}^{\text{8}}\text{m/s}\right)$ and represents the maximum velocity that light is able to travel through air.

Conversion of centimeter into meter (cm to m): $\text{1 cm}\text{=}{\text{1×10}}^{\text{-2}}\text{m}$

Explanation of Solution

The wavelength is $\text{2}\text{.0 cm}$

Conversion of centimeter to meter is,

$\begin{array}{l}\text{1 cm}\text{=}{\text{1×10}}^{\text{-2}}\text{m}\\ \\ \text{2}\text{.0 cm}\text{=}?\\ \\ =\frac{\left({\text{1×10}}^{\text{-2}}\text{m}\right)\left(2.0\text{cm}\right)}{\text{1 cm}}=2\times 10^{-2}m\end{array}$

Therefore, the given value of wavelength in meter is $2\times 10^{-2}m$ which fall in the region of Microwave region of the spectrum.

(b)

Interpretation Introduction

Interpretation:

The region of the electromagnetic spectrum for the given wavelength has to be specified.

Concept-Introduction:

Wavelength: The distance between successive peaks in a wave and measured in units of length.

Frequency: The number of waves passed a point in a certain amount of time.

Relation between wavelength and frequency:

$\text{Frequency}\left(\text{ν}\right)\text{=}\frac{\text{speed}\text{of}\text{light}\left(\text{c}\right)}{\text{wavelength}\left(\text{λ}\right)}$

Where, c is constant, the value of c is $\left(\text{3}{\text{.00×10}}^{\text{8}}\text{m/s}\right)$ and represents the maximum velocity that light is able to travel through air.

Conversion of micrometer into meter ($\mu m$ to m): $\text{1 μm}\text{=}{\text{1×10}}^{\text{-6}}\text{m}$

Explanation of Solution

The given wavelength is $\text{400}\text{nm}$

Conversion of nanometer to meter is,

$\begin{array}{l}\text{1 nm}\text{=}{\text{1×10}}^{\text{-9}}\text{m}\\ \\ \text{400}\text{nm}\text{=}?\\ \\ =\frac{\left({\text{1×10}}^{\text{-9}}\text{m}\right)\left(400nm\right)}{\text{1 nm}}=40\times 10^{-8}m\end{array}$

Therefore, the given value of wavelength in meter is $40\times 10^{-8}m$ which fall in the region of violet region of visiblelight of the spectrum. Because visible region begins from the range $10^{-6}-10^{-8}m$, so the obtained range falls at the violet color.

(c)

Interpretation Introduction

Interpretation:

The region of the electromagnetic spectrum for the given wavelength has to be specified.

Concept-Introduction:

Wavelength: The distance between successive peaks in a wave and measured in units of length.

Frequency: The number of waves passed a point in a certain amount of time.

Relation between wavelength and frequency:

$\text{Frequency}\left(\text{ν}\right)\text{=}\frac{\text{speed}\text{of}\text{light}\left(\text{c}\right)}{\text{wavelength}\left(\text{λ}\right)}$

Where, c is constant, the value of c is $\left(\text{3}{\text{.00×10}}^{\text{8}}\text{m/s}\right)$ and represents the maximum velocity that light is able to travel through air.

Conversion of nanometer into meter (nm to m): $\text{1 nm}\text{=}{\text{1×10}}^{\text{-9}}\text{m}$

Explanation of Solution

The wavelength is $\text{50}\mu \text{m}$

Conversion of micrometer to meter is,

$\begin{array}{l}\text{1 μm}\text{=}{\text{1×10}}^{\text{-6}}\text{m}\\ \\ \text{50 }\mu \text{m}\text{=}?\\ \\ =\frac{\left({\text{1×10}}^{\text{-6}}\text{m}\right)\left(50\mu m\right)}{\text{1 }\mu \text{m}}=50\times 10^{-6}m\end{array}$

Therefore, the given value of wavelength in meter is $50\times 10^{-6}m$ which fall in the region of visible region of the spectrum.

(d)

Interpretation Introduction

Interpretation:

The region of the electromagnetic spectrum for the given wavelength has to be specified.

Concept-Introduction:

Wavelength: The distance between successive peaks in a wave and measured in units of length.

Frequency: The number of waves passed a point in a certain amount of time.

Relation between wavelength and frequency:

$\text{Frequency}\left(\text{ν}\right)\text{=}\frac{\text{speed}\text{of}\text{light}\left(\text{c}\right)}{\text{wavelength}\left(\text{λ}\right)}$

Where, c is constant, the value of c is $\left(\text{3}{\text{.00×10}}^{\text{8}}\text{m/s}\right)$ and represents the maximum velocity that light is able to travel through air.

Conversion of millimeter into nanometer (mm to m): $\text{1 mm}\text{=}{\text{1×10}}^{\text{-3}}\text{m}$

Explanation of Solution

The given wavelength is $\text{150}\text{mm}$

Conversion of millimeter to meter is,

$\begin{array}{l}\text{1 mm}\text{=}{\text{1×10}}^{\text{-3}}\text{m}\\ \\ \text{150}\text{mm}\text{=}\text{?}\\ \\ \text{=}\frac{\left({\text{1×10}}^{\text{-3}}\text{m}\right)\left(\text{150 mm}\right)}{\text{1 mm}}\text{=}15\times 10^{-2}m\end{array}$

Therefore, the given value of wavelength in meter is $15\times 10^{-2}m$ which fall in the region of microwave region of the spectrum.