Chapter 3, Problem 1SAQ

Which wavelength of light has the highest frequency?

• 10 nm
• 10 mm
• 1 mm
• 1 nm

Interpretation Introduction

Interpretation:

The wavelength of light that has highest frequency should be determined.

Concept introduction: The frequency and wavelength are related as follows:

  $\text{c }=\nu \lambda$      - (1)

Rearranging:

  $\nu =\frac{c}{\lambda }$     - (2)

c is the velocity of light

  $\nu$ is the frequency

λ is the wavelength

Answer to Problem 1SAQ

Solution:

1 nm that is option (d) is present with highest frequency.

Explanation of Solution

Converting all the wavelengths to meter:

  $\begin{array}{l}\text{1}0\text{ nm }=\text{ 1}{0}^{-\text{8}}\text{m}\\ \text{1}0\text{ mm }=\text{ 1}{0}^{-\text{2}}\text{m}\\ \text{1 mm }=\text{ 1}{0}^{-\text{3}}\text{m}\\ \text{1 nm }=\text{ 1}{0}^{-\text{9}}\text{m}\end{array}$

From equation (2), it is clear that wavelength and frequency are inversely proportional to each other so, the wavelength with lower value will have greatest frequency of all. Thus, 1 nm is the lowest of all and is present with highest frequency.

Conclusion

1 nm that is option (d) is present with highest frequency.