Chapter U5.114, Problem 4E

Interpretation Introduction

(a)

Interpretation:

The wavelength of a light needs that has a frequency of $\text{4}{\text{.1×10}}^{\text{14}}\text{ Hz}$ to be determined.

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 4E

The wavelength of a light that has a frequency of $\text{4}{\text{.1×10}}^{\text{14}}\text{ Hz}$ is $\text{7}{\text{.32×10}}^{-7}\text{ m}$.

Explanation of Solution

Rearranging the formula (1) as:

$\text{λ = }\frac{\text{c}}{\nu }$ - (2)

Frequency, $\nu \text{ = 4}{\text{.1×10}}^{\text{14}}\text{ Hz}$ (given)

Substituting the values in formula (2):

$\begin{array}{l}\nu \text{ = }\frac{{\text{3×10}}^{\text{8}}\text{ m/sec}}{\text{4}{\text{.1×10}}^{\text{14}}{\text{ sec}}^{-1}}\\ \nu \text{ = 7}{\text{.32×10}}^{-7}\text{ m}\end{array}$

Hence, the wavelength of a light that has a frequency of $\text{4}{\text{.1×10}}^{\text{14}}\text{ Hz}$ is $\text{7}{\text{.32×10}}^{-7}\text{ m}$.

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 4E

The approximate color of the light is deep red.

Explanation of Solution

The wavelength of a light that has a frequency of $\text{4}{\text{.1×10}}^{\text{14}}\text{ Hz}$ is $\text{7}{\text{.32×10}}^{-7}\text{ m}$. On comparing these values, the approximate color of the light is deep red as the value of wavelength and frequency for deep red color is $\text{7}{\text{.5×10}}^{-7}\text{ m}$ and $\text{4}{\text{.0×10}}^{\text{14}}\text{ Hz}$ respectively.