Chapter 5, Problem 4STP

Interpretation Introduction

Interpretation: For the given change in wavelength of light the correct changes given in the option needs to be determined.

Concept Introduction: The wavelength of light is defined as the distance between the successive peaks of the wave of light. The frequency of a wave is defined as the number of peaks passing a point in one second.

Answer to Problem 4STP

The correct option is (C).

Explanation of Solution

Reason for correct option:

The relation between wavelength and energy of light is as follows:

  $E=\frac{hc}{\lambda }$

Here, h is Planck’s constant, c is the speed of light, and $\lambda$ is the wavelength of light.

The above equation can be rewritten as follows:

  $E\propto \frac{1}{\lambda }$

Thus, the wavelength is inversely proportional to the energy. As wavelength increases, the energy of light decreases.

Therefore, option (C) is correct.

Conclusion

Reason for incorrect options:

The correct relation between wavelength, frequency, and speed of the light is as follows:

  $v=\frac{c}{\lambda }$

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

In this relation, the speed of light is a constant; thus, it remains the same. The above formula can be rewritten as follows:

  $v\propto \frac{1}{\lambda }$

From the relation, the wavelength is inversely proportional to the frequency of light. Thus, if the wavelength of light increases, the frequency of light decreases.

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

Also, intensity and energy are directly proportional; thus, it is also inversely proportional to wavelength. Thus, as wavelength increases, the intensity of light decreases.

Therefore, option (D) is incorrect.