Chapter 1, Problem 1A.1AST

Interpretation Introduction

Interpretation:

The wavelengths of the light from traffic signals have to be calculated.

Concept Introduction:

The relationship between wavelength, frequency and speed of light is given below.

  $\lambda \times \nu =c$

Where, $\lambda$ is the wavelength, $\nu$ is the frequency of radiation and $c$ is the speed of light.

Answer to Problem 1A.1AST

The wavelengths of green, yellow, and red lights are $521nm$, $582nm$, and $702nm$ respectively.

Explanation of Solution

The traffic signal emits green, yellow and red lights.  It is given that the frequencies of green, yellow, and red lights are $5.75\times {10}^{14}Hz,5.15\times {10}^{14}Hzand4.27\times {10}^{14}Hz$ respectively.

The calculation of wavelengths of these lights can be done as shown below.

  $\begin{array}{l}{\lambda }_{Green}=\frac{c}{\nu }=\frac{3\times {10}^{8}m/s}{5.75\times {10}^{14}{s}^{-1}}=5.21\times {10}^{-7}m=521nm\\ \\ {\lambda }_{Yellow}=\frac{c}{\nu }=\frac{3\times {10}^{8}m/s}{5.15\times {10}^{14}{s}^{-1}}=5.82\times {10}^{-7}m=582nm\\ \\ {\lambda }_{\mathrm{Re}d}=\frac{c}{\nu }=\frac{3\times {10}^{8}m/s}{4.27\times {10}^{14}{s}^{-1}}=7.02\times {10}^{-7}m=702nm\\ \\ \left[\because 1nm={10}^{-9}m\right]\end{array}$

Therefore, the wavelengths of green, yellow, and red lights are $521nm$, $582nm$, and $702nm$ respectively.