Chapter 7, Problem 7.16P

(a)

Interpretation Introduction

Interpretation:

The frequency and the energy of the least energetic photon of UV radiation absorbed by oxygen molecules in the upper atmosphere are to be determined.

Concept introduction:

Electromagnetic waves are radiations that are formed by oscillating electric and magnetic fields. The electric and magnetic field components of an electromagnetic wave are perpendicular to each other.

The equation that relates to the frequency and wavelength of electromagnetic radiation is as follows:

$\nu =\frac{c}{\lambda }$        (1)

Here,

$c$ is the speed of light.

$\lambda$ is the wavelength.

$\nu$ is the frequency of the radiation.

Energy is proportional to the frequency and is expressed by the Plank-Einstein equation as follows:

$E=h\nu$

Here,

$E$ is the energy.

$h$ is the Plank’s constant.

$\nu$ is the frequency.

The above relation can be modified as follows:

$E=h\left(\frac{c}{\lambda }\right)$        (2)

The conversion factor to convert wavelength from $\text{nm}$ to $\text{m}$ is,

$1\text{nm}=1\times {10}^{-9}\text{ m}$

(b)

Interpretation Introduction

Interpretation:

The frequency and the energy of the most energetic photon absorbed by ozone molecules are to be determined.

Concept introduction:

Electromagnetic waves are radiations that are formed by oscillating electric and magnetic fields. The electric and magnetic field components of an electromagnetic wave are perpendicular to each other.

The equation that relates to the frequency and wavelength of electromagnetic radiation is as follows:

$\nu =\frac{c}{\lambda }$        (1)

Here,

$c$ is the speed of light.

$\lambda$ is the wavelength.

$\nu$ is the frequency of the radiation.

Energy is proportional to the frequency and is expressed by the Plank-Einstein equation as follows:

$E=h\nu$

Here,

$E$ is the energy.

$h$ is the Plank’s constant.

$\nu$ is the frequency.

The above relation can be modified as follows:

$E=h\left(\frac{c}{\lambda }\right)$        (2)

The conversion factor to convert wavelength from $\stackrel{\text{o}}{\text{A}}$ to $\text{m}$ is,

$1\stackrel{\text{o}}{\text{ A}}=1\times {10}^{-10}\text{ m}$