Chapter 5, Problem 63A

Interpretation Introduction

Interpretation : The wavelength of the radiation in centimeter is to be calculated.

Concept Introduction : The separation between the crests is known as the wavelength.

The frequency is how often waves cycle through a specific point in a unit of time.

Answer to Problem 63A

The wavelength of the radiation in centimeter is $4.36\times {10}^{-5}\text{cm}$ .

Explanation of Solution

Given information:

The wavelength is $4.36\times {10}^{-7}\text{m}$ .

It is known $1\text{m}\text{=}{\text{10}}^2\text{cm}$ .

The separation between the crests is known as the wavelength.

The frequency is how often waves cycle through a specific point in a unit of time.

With the help of unit conversion from meter to centimeter, the wavelength in centimeters is calculated.

  $\begin{array}{c}\lambda =4.36\times {10}^{-7}\text{m}\\ =4.36\times {10}^{-7}\cancel{\text{m}}\times \frac{{10}^2\text{cm}}{1\cancel{\text{m}}}\\ \lambda =4.36\times {10}^{-5}\text{cm}\end{array}$

The wavelength of the radiation is $4.36\times {10}^{-5}\text{cm}$ .

Interpretation Introduction

Interpretation : The region of the electromagnetic spectrum is to be identified.

Concept Introduction : A wide range of wavelengths of radiation make up the electromagnetic spectrum. It has a wavelength in the ${10}^{-7}\text{m}$ range and a frequency in the $\text{1015 Hz}$ range.

Answer to Problem 63A

The region of the electromagnetic spectrum is visible.

Explanation of Solution

A wide range of wavelengths of radiation makes up the electromagnetic spectrum.

It has a wavelength in the ${10}^{-7}\text{m}$ range and a frequency in the $\text{1015 Hz}$ range.

To find the region of the electromagnetic spectrum, the wavelength should be expressed in nanometers.

The wavelength in the nanometer is given as:

  $\begin{array}{c}\lambda =4.36\times {10}^{-7}\text{m}\\ =4.36\times {10}^{-7}\cancel{\text{m}}\times \frac{{10}^9\text{nm}}{1\cancel{\text{m}}}\\ \lambda =4.36\times {10}^2\text{nm}\\ \text{= }\text{436}\text{nm}\end{array}$

Since the value of wavelength is low, it belongs to a visible region whose range is in between $380\text{nm}$ and $\text{700}\text{nm}$ .

Interpretation Introduction

Interpretation : The frequency of the radiation is to be calculated.

Concept Introduction : The separation between the crests is known as the wavelength.

The frequency is how often waves cycle through a specific point in a unit of time.

The formula of frequency $\left(\nu \right)$ is given as:

  $\nu =\frac{c}{\lambda }$

Where $c$ is the velocity of light and $\lambda$ is the wavelength of the photon.

Answer to Problem 63A

The frequency of the radiation is $6.88\times {10}^{14}\text{Hz}$ .

Explanation of Solution

Given information:

The wavelength is $4.36\times {10}^{-7}\text{m}$ .

It is known that the velocity of light is $2.998\times {10}^8\text{m/s}$ .

The separation between the crests is known as the wavelength.

The frequency is how often waves cycle through a specific point in a unit of time.

The formula of frequency $\left(\nu \right)$ is given as:

  $\nu =\frac{c}{\lambda }$

Where $c$ is the velocity of light and $\lambda$ is the wavelength of the photon.

To calculate the frequency of radiation, substitute the values in the above formula.

  $\begin{array}{c}\nu =\frac{c}{\lambda }\\ =\frac{2.998\times {10}^8\cancel{\text{m}}\text{/s}}{4.36\times {10}^{-7}\cancel{\text{m}}}\\ =0.6876\times {10}^{15}{\text{s}}^{-1}\\ \nu =6.88\times {10}^{14}\text{Hz}\end{array}$

The frequency of the radiation is $6.88\times {10}^{14}\text{Hz}$ .