Chapter 5, Problem 52A

Interpretation Introduction

Interpretation : The energy of a photon of green light is to be calculated.

Concept Introduction : Planck demonstrated mathematically that a body's ability to absorb or emit radiation is inversely related to the frequency of the radiation (v). The formula of energy is given as:

  $E=h\nu$

Where $\text{h}$ is Planck’s constant and $\nu$ is the frequency of the photon.

Answer to Problem 52A

The energy of a photon of green light is $\text{3}\text{.84}\times {\text{10}}^{-19}\text{J}$ .

Explanation of Solution

Given information:

The frequency is $5.80\times {10}^{14}\text{/s}$ .

It is known that the value of Planck’s constant is $\text{h}\text{=}6.626\times {10}^{-34}\text{J}\text{s}$ .

Planck demonstrated mathematically that a body's ability to absorb or emit radiation is inversely related to the frequency of the radiation (v).

The formula of energy is given as:

  $E=h\nu$

Where $\text{h}$ is Planck’s constant and $\nu$ is the frequency of the photon.

To calculate the energy of a photon, substitute the values in the above formula.

  $\begin{array}{c}E=h\nu \\ =\left(6.626\times {10}^{-34}\text{J}\cancel{\text{s}}\right)\times \left(5.80\times {10}^{14}\cancel{{\text{s}}^{-1}}\right)\\ =38.430\times {10}^{-20}\text{J}\\ E=\text{ 3}\text{.84}\times {\text{10}}^{-19}\text{J}\end{array}$

The energy of a photon of green light is $\text{3}\text{.84}\times {\text{10}}^{-19}\text{J}$ .