Chapter U5, Problem 20STP

Interpretation Introduction

Interpretation:

The true statement about the blue light needs to be determined, if red light has a wavelength of $\text{7}\text{.5}\times {\text{10}}^{\text{-7}}$ m and a frequency $\text{4}\text{.0}\times {\text{10}}^{14}$ Hz.

Concept introduction:

Electromagnetic radiations can be defined as radiations of electromagnetic field. These are the radiations of electromagnetic field which propagate through space and have certain electromagnetic energy.

Different electromagnetic radiations are X-rays, Infra-red, Ultra-violet, radio waves, and microwaves.

Each radiation is associated with certain energy, frequency and wavelength. The relation between energy, frequency and wavelength is:

$\begin{array}{l}\text{E = h × }\upsilon \text{ = }\frac{\text{h × c}}{\lambda }\\ \text{E = energy}\\ \upsilon \text{ = Frequency}\\ \text{h = Plank's constant}\\ \lambda \text{ = wavelength}\\ \text{c = Speed of light}\end{array}$

Answer to Problem 20STP

Option (A) is the correct option.

Explanation of Solution

Reason for correct option:

Wavelength of red light = $\text{7}\text{.5}\times {\text{10}}^{\text{-7}}$ m

Frequency of red light = $\text{4}\text{.0}\times {\text{10}}^{14}$ Hz

The wavelength of blue light shorter than red light. Since wavelength is inversely proportional to energy, therefore, the energy and frequency of blue light must be higher than red light.

Conclusion

Reasons for incorrect options: The speed of light remains constant, whereas energy and frequency of radiations depends on wavelength.

Since wavelength of blue light is shorter than red light, thus energy and frequency of blue light must be higher than red light.