Chapter U5.114, Problem 5E

Interpretation Introduction

(a)

Interpretation:

The frequency of a light needs to be determined that has a wavelength of $\text{5}{\text{.1×10}}^{-7}\text{ m}$.

Concept introduction:

The formula which relates frequency of the light and the wavelength of the light is:

$\nu \text{ = }\frac{\text{c}}{\text{λ}}$ - (1)

Where v is the frequency of the light, c is velocity of light ( ${\text{3×10}}^{\text{8}}\text{ m/sec}$ ), and λ is wavelength of the light.

Answer to Problem 5E

The frequency of a light that has a wavelength of $\text{5}{\text{.1×10}}^{-7}\text{ m}$ is $\text{5}{\text{.88×10}}^{14}\text{ Hz}$.

Explanation of Solution

The formula which relates frequency of the light and the wavelength of the light is:

$\nu \text{ = }\frac{\text{c}}{\text{λ}}$ - (1)

Wavelength, $\lambda =\text{ 5}{\text{.1×10}}^{-7}\text{ m}$ (given)

Substituting the values in formula (2):

$\begin{array}{l}\nu \text{ = }\frac{{\text{3×10}}^{\text{8}}\text{ m/sec}}{\text{5}{\text{.1×10}}^{-7}\text{ m}}\\ \nu \text{ = 5}{\text{.88×10}}^{14}\text{ Hz}\end{array}$

Hence, the frequency of a light that has a wavelength of $\text{5}{\text{.1×10}}^{-7}\text{ m}$ is $\text{5}{\text{.88×10}}^{14}\text{ Hz}$.

Interpretation Introduction

(b)

Interpretation:

The approximate color of the light needs to be determined.

Concept introduction:

The light waves possess different colors which are characterized by wavelengths and frequencies. All the light waves move at the same speed, that is speed of light.

Answer to Problem 5E

The approximate color of the light is yellow-green.

Explanation of Solution

The frequency of a light that has a wavelength of $\text{5}{\text{.1×10}}^{-7}\text{ m}$ is $\text{5}{\text{.88×10}}^{14}\text{ Hz}$. On comparing these values, the approximate color of the light is yellow-green as the value of wavelength and frequency for yellow-green color is $\text{5}{\text{.5×10}}^{-7}\text{ m}$ and $\text{5}{\text{.5×10}}^{\text{14}}\text{ Hz}$.