Chapter 5, Problem 5.137MP

Interpretation Introduction

(a)

Interpretation:

The frequency of the photon produced by an X-ray machine having an energy of $4.70\times {10}^{-16}\text{J}$ needs to be determined.

Concept introduction:

Electromagnetic radiation can be defined as the waves of the electromagnetic field which can propagate through space and also carries the electromagnetic radiant energy. Radio waves, microwaves, infrared, light, ultraviolet, X-rays, and gamma rays are some common example of electromagnetic radiations. The relation between the wavelength, energy and frequency of the electromagnetic radiations is as given below:

$\begin{array}{l}\text{E = hν = }\frac{\text{hc}}{\text{λ}}\\ \text{Here:}\\ \text{ν = frequency}\\ \text{c = speed of light }\\ \text{λ = wavelength}\\ \text{h= Planck's constant }\\ \text{E = energy}\end{array}$

Interpretation Introduction

(b)

Interpretation:

The wavelength of the photon with frequency $\text{7}{\text{.09 ×10}}^{\text{17 }}\text{Hz}$ needs to be determined.

Concept introduction:

Electromagnetic radiation can be defined as the waves of the electromagnetic field which can propagate through space and carries the electromagnetic radiant energy. Radio waves, microwaves, infrared, light, ultraviolet, X-rays, and gamma rays are some common example of electromagnetic radiations. The relation between the wavelength, energy and frequency of the electromagnetic radiations is as given below:

$\begin{array}{l}\text{E = hν = }\frac{\text{hc}}{\text{λ}}\\ \text{Here:}\\ \text{ν = frequency}\\ \text{c = speed of light }\\ \text{λ = wavelength}\\ \text{h= Planck's constant }\\ \text{E = energy}\end{array}$

Interpretation Introduction

(c)

Interpretation:

The velocity with de Broglie wavelength of $\text{λ = 4}{\text{.23×10}}^{\text{-10}}\text{m}$ needs to be determined.

Concept introduction:

Electromagnetic radiation can be defined as the waves of the electromagnetic field which can propagate through space and carries electromagnetic radiant energy. Radio waves, microwaves, infrared, light, ultraviolet, X-rays, and gamma rays are some common examples of electromagnetic radiation. The relation between the wavelength, energy and frequency of the electromagnetic radiations is as given below:

$\begin{array}{l}\text{E = hν = }\frac{\text{hc}}{\text{λ}}\\ \text{Here:}\\ \text{ν = frequency}\\ \text{c = speed of light }\\ \text{λ = wavelength}\\ \text{h= Planck's constant }\\ \text{E = energy}\end{array}$

The de Broglie equation purposed the relation between wavelength and mass of the photon. The mathematical expression for this relation is:

$\text{λ = }\frac{\text{h}}{\text{m×v}}$

Here:

• v = velocity
• h = Planck’s constant
• λ = wavelength

Interpretation Introduction

(d)

Interpretation:

The kinetic energy with a moving electron of velocity $\text{v =1}{\text{.72×10}}^{\text{6}}\text{m/sec}$ needs to be determined.

Concept introduction:

Electromagnetic radiation can be defined as the waves of the electromagnetic field which can propagate through space and carries electromagnetic radiant energy. Radio waves, microwaves, infrared, light, ultraviolet, X-rays, and gamma rays are some common examples of electromagnetic radiation. The relation between the wavelength, energy and frequency of the electromagnetic radiations is as given below:

$\begin{array}{l}\text{E = hν = }\frac{\text{hc}}{\text{λ}}\\ \text{Here:}\\ \text{ν = frequency}\\ \text{c = speed of light }\\ \text{λ = wavelength}\\ \text{h= Planck's constant }\\ \text{E = energy}\end{array}$

The de Broglie equation purposed the relation between wavelength and mass of the photon. The mathematical expression for this relation is:

$\text{λ = }\frac{\text{h}}{\text{m×v}}$

Here:

• v = velocity
• h = Planck’s constant
• λ = wavelength