Chapter 5, Problem 1STP

Interpretation Introduction

Interpretation:

The frequency of cosmic rays having a wavelength of $2.67\times {10}^{-13}\text{m}$ when it reaches to earth. (The speed of light is $3.00\times {10}^8\text{m/s}$ ) needs to be determined.

Concept introduction:

The wavelength of a light is defined as the distance between two consecutive crest and trough in the wave. The frequency of light is a number of cycles of the light passing through a given point in one second.

Formula used:

$\text{E}=\text{h}v\text{and}v=\frac{c}{\text{λ}}$

Where, E represents the energy of the light, h represents the Plank’s constant, c is the speed of the light, λ is the wavelength of light and ν is the frequency of light.

Answer to Problem 1STP

The correct option is D.

Explanation of Solution

To determine the frequency of the cosmic rays, divide the speed of light by wavelength.

$\begin{array}{c}\text{Frequency}=\frac{\text{Speed}\text{of}\text{light}}{\text{Wavelength}}\\ =\frac{3.00\times {10}^8\text{m/s}}{2.67\times {10}^{-13}\text{m}}\\ =1.12\times {10}^{21}{\text{s}}^{-1}\end{array}$

Hence, the frequency of the cosmic rays is $1.12\times {10}^{21}{\text{s}}^{-1}$.

Conclusion

The frequency of the cosmic rays is $1.12\times {10}^{21}{\text{s}}^{-1}$. Hence, the correct option is D.