Chapter 5, Problem 62A

Interpretation Introduction

Interpretation : The wavelength of the radiation from the station 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 wavelength $\left(\lambda \right)$ is given as:

  $\lambda =\frac{c}{\nu }$

Where $c$ is the velocity of light and $\nu$ is the frequency of the photon.

Answer to Problem 62A

The wavelength of the radiation is $2.61\times {10}^4\text{cm}$ .

Explanation of Solution

Given information:

The frequency is $1150\text{kHz}$ . It is equal to $1150\times {10}^3{\text{s}}^{-1}\left(\because \text{Hz}\text{=}{\text{s}}^{-1}\right)$ .

It is known that the velocity of light is $c=\text{2}\text{.998}\times {\text{10}}^{10}\text{cm/s}$ .

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 wavelength $\left(\lambda \right)$ is given as:

  $\lambda =\frac{c}{\nu }$

Where $c$ is the velocity of light and $\nu$ is the frequency of the photon.

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

  $\begin{array}{c}\lambda =\frac{c}{\nu }\\ =\frac{\left(2.998\times {10}^{10}\text{cm/}\cancel{\text{s}}\right)}{1150\times {10}^3\cancel{{\text{s}}^{-1}}}\\ \lambda =2.61\times {10}^4\text{cm}\end{array}$

The wavelength of the radiation is $2.61\times {10}^4\text{cm}$ .