Chapter 7, Problem 1SAQ

Which wavelength of light has the highest frequency?

a) 10 nm

b) 10 mm

c) 1 nm

d) 1 mm

Interpretation Introduction

To determine: The wavelength having the highest frequency.

Answer to Problem 1SAQ

Correct answer: The highest frequency will be for $1\text{ nm}$ wavelength of light. So, the correct answer is option (c).

Explanation of Solution

Justify the reasons for the correct statement:

Frequency $\left(v\right)$ and wavelength $\left(\lambda \right)$ are inversely related to each other. Their relation is as follows:

$v=\frac{1}{\lambda }$

The wavelength of light is $1\text{ nm}$. So, the wavelength in meters will be as follows:

$\begin{array}{c}\lambda =1\text{ nm}\left(\frac{{10}^{-9}\text{ m}}{1\text{ nm}}\right)\\ ={10}^{-9}\text{ m}\end{array}$

This is the shortest wavelength. So, it will have the highest frequency.

Hence, option (c) is correct.

Justify reasons for the incorrect statements:

Option (a) is given as $10\text{ nm}$.

The wavelength of light is $10\text{ nm}$. So, the wavelength in meters will be as follows:

$\begin{array}{c}\lambda =10\text{ nm}\left(\frac{{10}^{-9}\text{ m}}{1\text{ nm}}\right)\\ ={10}^{-8}\text{ m}\end{array}$

So, it is an incorrect answer.

Option (b) is given as $10\text{ mm}$.

The wavelength of light is $10\text{ mm}$. So, the wavelength in meters will be as follows:

$\begin{array}{c}\lambda =10\text{ mm}\left(\frac{{10}^{-3}\text{ m}}{1\text{ mm}}\right)\\ ={10}^{-2}\text{ m}\end{array}$

So, it is an incorrect answer.

Option (d) is given as $1\text{ mm}$.

The wavelength of light is $1\text{ mm}$. So, the wavelength in meters will be as follows:

$\begin{array}{c}\lambda =1\text{ mm}\left(\frac{{10}^{-3}\text{ m}}{1\text{ mm}}\right)\\ ={10}^{-3}\text{ m}\end{array}$

So, it is an incorrect answer.

Hence, options (a), (b), and (d) are incorrect.

Conclusion

The correct answer is option (c).