Chapter 3, Problem 3.125QP

Interpretation Introduction

Interpretation:

The wavelength and frequency of an emitted photon of gamma having the energy of $\text{3}{\text{.14 × 10}}^{\text{11}}\text{ J/mol}$ 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 the distance between identical points on successive waves.  The frequency is the number of waves that pass through any particular point in 1 second.

Figure 1

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

Planck’s quantum theory

• Different atoms and molecules can emit or absorb energy in discreet quantities only.  The smallest amount of energy that can be emitted or absorbed in the form of electromagnetic radiation is known as quantum.
• 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 ($6.626\times {10}^{–34}\text{ Js}$); $\text{ν}$ = frequency of radiation.

To find: Calculate the wavelength and frequency of an emitted gamma photon having the energy of $\text{3}{\text{.14 × 10}}^{\text{11}}\text{ J/mol}$