Chapter 11.1, Problem 6RQ

Interpretation Introduction

Interpretation: A relationship between the wavelength of light and the energy of its photons needs to be derived.

Concept Introduction: The energy of a photon is dependent on the frequency of wave. The wavelength of a wave is also dependent on the energy of the wave.

Answer to Problem 6RQ

The relationship between wavelength and wave energy is given by the following equation:

  $E=\frac{hc}{\lambda }(\text{h is Planck's constant, c is speed of light, }\lambda \text{ is wavelength)}$

Explanation of Solution

The wavelength of a wave is the ratio of its wave speed and frequency, i.e.:

  $\begin{array}{l}\lambda =\frac{c}{\upsilon }(\upsilon \text{ is frequency,c is speed of light,}\lambda \text{ is wavelength)}\\ \upsilon \text{=}\frac{c}{\lambda }\end{array}$

According to Planck’s wave energy equation,

  $E=h\upsilon$

Substituting the value of frequency,

  $E=\frac{hc}{\lambda }$

Which is the required relation.