Chapter 5, Problem 12STP

Interpretation Introduction

Interpretation: The drawing showing the electromagnetic wave with the highest energy needs to be identified.

Concept Introduction: When an electric field and a magnetic field are coupled together, an electromagnetic wave is formed. Here, electric and magnetic fields are perpendicular to each other as well as the direction of the wave.

Here, the wavelength of a wave is defined as the distance between two successive crests and troughs. The frequency of a wave is the number of waves passing a point in one second. The amplitude of a wave is determined by the height of the crests and troughs formed in the electromagnetic waves.

Moreover, the energy of the wave is inversely proportional to its wavelength. This can be explained by the following formula:

  $E=\frac{hc}{\lambda }$

Here, h is Planck’s constant and c is the speed of light. Both are constant; thus, the above relation can be rewritten as follows:

  $E\propto \frac{1}{\lambda }$

Here, E is energy and $\lambda$ is the wavelength of light.

Answer to Problem 12STP

Correct answer is option (C).

Explanation of Solution

Reason for correct option:

The wave with the shortest wavelength will have the smallest distance between two successive crests and the trough of the wave.

The wave with the smallest distance is shown below:

  

Since wavelength is inversely proportional to energy thus, the above wave has the highest energy.

Thus, the correct option is (C).

Conclusion

Reason for incorrect options:

From the given drawings, drawing in option (A) has a wave with the longest wavelength because there the distance between two successive crests and trough is large.

  

Thus, it has the lowest energy as the wavelength is inversely proportional to the energy.

The wave shown in option (B) is as follows:

  

On comparing with the wave in option (C), the wavelength is more; thus, this is also an incorrect option.

Thus, options (A) and (B) are incorrect.