Chapter 7, Problem 7.16QP

(a)

Interpretation Introduction

Interpretation:

The wavelength (in nanometers) associated with the blue radiation and the energy (in joules) of a single photon associated with the frequency of $\text{7}{\text{.5 × 10}}^{\text{14}}\text{ Hz}$ should be calculated using the relation between speed, wavelength and frequency of a wave and Planck’s quantum theory.

Concept Introduction:

A wave is a disturbance or variation that travels through a medium transporting energy without transporting matter.  The wavelength is defined as the distance between the two similar points on consecutive waves.  The frequency is defined as the number of waves which move through any particular point in one second.

Figure.1

The speed, wavelength and frequency of a wave are interrelated by $\text{c }=\text{ λν}$ where $\text{λ and ν}$ are mentioned in meters ($\text{m}$) and reciprocal seconds (${\text{s}}^{-1}$).

Planck’s quantum theory

1. 1. Different atoms or molecules emit or absorb energy in discreet quantities only.  The smallest amount of energy which is emitted or absorbed in the form of electromagnetic radiation is called quantum.
2. 2. The energy of the radiation absorbed or emitted is directly proportional to the frequency of the radiation.  The energy of radiation is expressed in terms of frequency as, $\text{E }=\text{ hν}$ where, $\text{E}$ = energy of the radiation; $\text{h}$ = Planck’s constant ($6.626\times {10}^{–34}\text{ Js}$) and $\text{ν}$ = frequency of radiation.

(b)

Interpretation Introduction

Interpretation:

The wavelength (in nanometers) associated with the blue radiation and the energy (in joules) of a single photon associated with the frequency of $\text{7}{\text{.5 × 10}}^{\text{14}}\text{ Hz}$ should be calculated using the relation between speed, wavelength and frequency of a wave and Planck’s quantum theory.

Concept Introduction:

A wave is a disturbance or variation that travels through a medium transporting energy without transporting matter.  The wavelength is defined as the distance between the two similar points on consecutive waves.  The frequency is defined as the number of waves which move through any particular point in one second.

Figure.1

The speed, wavelength and frequency of a wave are interrelated by $\text{c }=\text{ λν}$ where $\text{λ and ν}$ are mentioned in meters ($\text{m}$) and reciprocal seconds (${\text{s}}^{-1}$).

Planck’s quantum theory

1. 1. Different atoms or molecules emit or absorb energy in discreet quantities only.  The smallest amount of energy which is emitted or absorbed in the form of electromagnetic radiation is called quantum.
2. 2. The energy of the radiation absorbed or emitted is directly proportional to the frequency of the radiation.  The energy of radiation is expressed in terms of frequency as, $\text{E }=\text{ hν}$ where, $\text{E}$ = energy of the radiation; $\text{h}$ = Planck’s constant ($6.626\times {10}^{–34}\text{ Js}$) and $\text{ν}$ = frequency of radiation.

To find: Calculate the energy (in joules) of a single photon