Chapter 5.1, Problem 1PP

Interpretation Introduction

Interpretation:

The frequency of the light needs to be calculated having a wavelength of $4.90\times {10}^{-7}\mathrm{m}$ .

Concept introduction:

The number of times a wave passed through a point in 1 section is known as the frequency of the wave. It is denoted by the symbol $\nu$ with a unit per second or Hz.

It is related to the speed of light and wavelength as follows:

  $\nu =\frac{c}{\lambda }$

Here, c is the speed of light and $\lambda$ is the wavelength.

Answer to Problem 1PP

Frequency of the light $=6.122\times {10}^{14}{\sec }^{-1}$ .

Explanation of Solution

Given Information:

Wavelength of light $=4.90\times {10}^{-7}\text{m}$

Calculation:

The frequency is related to the speed of light and wavelength as follows:

  $\nu =\frac{c}{\lambda }$

V = Frequency

c = velocity of light $\left(3\times {10}^8{\text{ms}}^{-1}\right)$

  $\lambda$ = wavelength

Putting the values,

  $\nu =\frac{c}{\lambda }$

  $\nu \text{=}\frac{{\text{3×10}}^{\text{8}}\text{m/s}}{\text{4}{\text{.9×10}}^{\text{-7}}\text{m}}$

  $\nu =\frac{3\times {10}^{8+7}}{4.9}$

  $\nu =\frac{300\times {10}^{14}}{49}$

  $=6.122\times {10}^{14}{\sec }^{-1}$

Conclusion

Thus, the frequency of the light $=6.122\times {10}^{14}{\sec }^{-1}$ having a wavelength of $4.90\times {10}^{-7}\text{m}$ .