Chapter 28, Problem 42A

a.

To determine

To calculate: The energy difference between the two states involved in the generation of each wavelength.

Answer to Problem 42A

Energy change for $632.8\text{ nm}$ is $\underset{\_}{1.96\text{ eV}}$

Energy change for $\text{543}\text{.4 nm}$ is $\underset{\_}{\text{2}\text{.28 eV}}$

Energy change for $\text{1152}\text{.3 nm}$ is $\underset{\_}{\text{1}\text{.08 eV}}$

Explanation of Solution

Given:

Wavelengths of the laser = $632.8\text{ nm,543}\text{.4 nm, 1152}\text{.3 nm}$ .

Formula used:

Energy change is given by,

  $\Delta E=\frac{hc}{\lambda }$

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

Calculation:

For $632.8\text{ nm}$ , energy change is calculated as:

  $\begin{array}{l}\Delta E=\frac{hc}{\lambda }\text{ [}hc=1240\text{ eV}\cdot \text{nm}]\\ \text{ =}\frac{1240\text{ eV}\cdot \text{nm}}{632.8\text{ nm}}\\ =1.96\text{ eV}\end{array}$

For $\text{543}\text{.4 nm}$ , energy change is calculated as:

  $\begin{array}{l}\Delta E=\frac{hc}{\lambda }\text{ [}hc=1240\text{ eV}\cdot \text{nm}]\\ \text{ =}\frac{1240\text{ eV}\cdot \text{nm}}{\text{543}\text{.4 nm}}\\ =2.28\text{ eV}\end{array}$

For $\text{1152}\text{.3 nm}$ , energy change is calculated as:

  $\begin{array}{l}\Delta E=\frac{hc}{\lambda }\text{ [}hc=1240\text{ eV}\cdot \text{nm}]\\ \text{ =}\frac{1240\text{ eV}\cdot \text{nm}}{\text{1152}\text{.3 nm}}\\ =1.08\text{ eV}\end{array}$

Conclusion:

Energy change for $632.8\text{ nm}$ is $\underset{\_}{1.96\text{ eV}}$

Energy change for $\text{543}\text{.4 nm}$ is $\underset{\_}{\text{2}\text{.28 eV}}$

Energy change for $\text{1152}\text{.3 nm}$ is $\underset{\_}{\text{1}\text{.08 eV}}$

b.

To determine

To identify: The color corresponding to each wavelength.

Explanation of Solution

Introduction:

The portion of electromagnetic spectrum that is visible to human eye is called electromagnetic spectrum. A typical human eye can see $380\text{ nm -740 nm}$ . Infrared lights have wavelengths longer than those of visible light.

The colors according to their wavelength are:

  

Hence the wavelength $632.8\text{ nm}$ corresponds to red light, $\text{543}\text{.4 nm}$ corresponds to green light and $\text{1152}\text{.3 nm}$ corresponds to infrared light.

Conclusion:

The colors are Red, Green and Infrared respectively.