Chapter 7, Problem 1RQ

Four types of electromagnetic radiation (EMR) are ultraviolet, microwaves, gamma rays, and visible. All of these types of EMR can be characterized by wavelength, frequency, photon energy, and speed of travel. Define these terms and rank the four types of electromagnetic radiation in order of increasing wavelength, frequency, photon energy, and speed.

Interpretation Introduction

Interpretation:

All the given four types of electromagnetic radiations (EMR). that are ultraviolet, microwave, gamma rays, and visible can be characterized by wavelength, frequency, photon energy and speed of travel. All these are to be defined. The given four types of electromagnetic radiations are to be ranked in order of increasing wavelength, frequency, photon energy and speed.

Concept introduction:

Basically electromagnetic radiation is an energy form which is present all around us and it can takes many other forms such radio waves, microwaves, $\text{γ}$-rays, $\text{X}$-rays, visible light, ultraviolet light. Sun light is also a very common form of electromagnetic energy. In all these forms visible light takes a very small portion of all the electromagnetic radiations. The characterization of all these forms is based on some mathematical and physical formula.

To determine: The definitions of the given terms and the ranking of the given terms in the increasing order of wavelength, frequency, photon energy and speed.

Answer to Problem 1RQ

Answer

The definition of the stated terms, that is wavelength, frequency, photon energy and speed has been rightfully stated.

The correct ranking of the given terms in order of increasing wavelength is,

$\text{Gamma}\text{rays}<\text{Ultraviolet}<\text{Visible}<\text{Microwaves}$

The correct ranking of the given terms in order of increasing frequency is,

$\text{Microwaves}<\text{Visible}<\text{Ultraviolet}<\text{Gamma}\text{rays}$

The correct ranking of the given terms in order of increasing photon energy is,

$\text{Microwaves}<\text{Visible}<\text{Ultraviolet}<\text{Gamma}\text{rays}$

All the electromagnetic radiations travel at the same speed that is speed of light.

Explanation of Solution

Explanation

The given terms have been defined as follows.

Wavelength is defined as the distance between the consecutive troughs or the crest of a sinusoidal wave.

Frequency is defined as the repetition of any phenomena over a certain period of time

The amount of energy present in photon is termed as photon energy.

Transmission of electromagnetic radiations to a certain distance over a certain period of time is called a speed for electromagnetic radiations.

All the electromagnetic radiations are basically a form of energy that behave as a travelling wave. Every wave has specific wavelength, frequency, energy, and speed so all the radiations have the same wave nature.

Wavelength is the length of the wave and it is denoted by the term $\text{λ}$.

Frequency is the repetition of the wave in a certain period of time and is denoted by the term $\text{υ}$.

Photon energy is the energy of photon which is the smallest unit of energy and the speed of the wave is distance covered by the wave in a particular time period.

The ranking of the given terms in the increasing order of wavelength, frequency, photon energy and speed

The relationship between wavelength, frequency, photon energy, and speed is stated in the following figure.

Figure 1

The Figure 1 shows an increasing order of wavelength. Wavelength is related to frequency by the relationship known as the Planck’s-Einstein relationship.

$\begin{array}{l}E=h\upsilon \\ \upsilon =\frac{c}{\lambda }\end{array}$

This shows that frequency and wavelength are inversely proportional to each other while energy is directly proportional to frequency and inversely proportional to the wavelength. Sped of all the electromagnetic radiations is same because all are a form of energy.

Conclusion

All the electromagnetic radiations are basically a form of energy that behave as a travelling wave. Every wave has specific wavelength, frequency, energy, and speed so all the radiations have the same wave nature.