In this chapter, we will understand the wave nature of electromagnetic radiation with its definition, characteristics, and examples.
We know that light is an important form of energy. Isaac Newton proposed the corpuscular theory of light, which regarded the light as a stream of particles, or corpuscles. This particle nature of light could able to explain the phenomenon of reflection and refraction of light, but failed to explain other important behaviors of light, such as interference and diffraction.
Therefore, Newton’s corpuscular theory of light was eventually discarded and replaced by the wave theory of light proposed by Christiaan Huygens. This wave theory of light was able to explain the phenomenon that the corpuscular theory could not, such as interference, diffraction, and polarization of light.
What is Electromagnetic Radiation?
James Clerk Maxwell in 1856 proposed that light and other forms of energy radiations, such as visible, ultraviolet, infrared, X-rays, gamma rays, etc. propagate through space in the form of waves. These waves have both electrical and magnetic fields associated with them and travel at the right angle to these fields (i.e. oscillate perpendicular to each other).
Because of the involvement of both electric and magnetic fields, they are called electromagnetic radiation or electromagnetic waves. Thus, light and other form of radiant energy can be transmitted through space by electromagnetic radiations. Some forms of radiant energy are radio waves, visible light, infrared light, ultraviolet light, X-rays and γ-radiations. They do not need any medium for propagation, meaning they can travel through the vacuum of space.
Characteristics of Electromagnetic Radiation or Wave
An electromagnetic radiation is generated when electrically charged particle moves under acceleration, alternating electrical and magnetic fields are produced and transmitted. These fields are transmitted in the forms of waves called electromagnetic waves or electromagnetic radiation.
The below figure shows the propagation of electromagnetic radiation in the form of waves.
To understand the wave nature of electromagnetic radiation, it is important to understand the important characteristics of electromagnetic radiation.
- All electromagnetic radiations travel with the velocity of light (3 * 108 ms-1 or 3 * 1010 cms-1) in vacuum.
- These radiations do not require any medium to travel.
- These consist of electric and magnetic fields that oscillate at the right angle to each other and perpendicular to the direction in which the wave is propagating or travelling.
- The energy of electromagnetic radiation is directly proportional to its frequency and inversely proportional to its wavelength.
Wave Characteristics
A electromagnetic wave or radiation is always characterized by the following six characteristics:
(i) Wavelength: The straight distance between two nearest crests or nearest troughs of a wave is called the wavelength. It is denoted by the Greek letter λ (lambda) and is measured in terms of centimetre (cm), angstrom (A), micrometre (µm) or nanometre (nm).
- One angstrom, Å, is equal to 10–8 cm or 10-10 m
- 1nm = 10–9 m = 10-7 cm
- 1µm = 10-4 cm = 10-6 m
- 1 cm = 108 Å = 104 µm = 107 nm
- 1 m = 1010 Å
(ii) Frequency: The number of times a wave passes through a given point in one second is known as frequency of the wave. It is denoted by the symbol v (Greek letter nu)) and is measured in terms of cycles (or waves) per second (cps) or hertz (Hz) units. One Hz = 1 cycle/s.
Mathematically,
Frequency (v) = c / λ where, c = velocity of the radiation and λ = wavelength of the radiation
Thus, Frequency (v) = velocity of the radiation / wavelength of the radiation
(iii) Velocity: The distance travelled by a particular wave in one second is called velocity or speed of the wave. It is denoted by the letter ‘c’ and it is measured in cm per second (cm/s). If the velocity of a wave is c cm/sec, it means that the distance travelled by the wave in one second is c cm.
Velocity of the electromagnetic radiation is related to the frequency and wavelength by the expression c = νλ.
Or, Velocity of radiation (c) = frequency × wavelength
The various types of electromagnetic radiations have different frequencies and wavelengths, but travel with the same speed or velocity, i. e. , 3 x 1010 cm/sec or 186,000 miles per second which is, in fact, the velocity of light.
Thus, a electromagnetic wave or radiation of higher frequency has a shorter wavelength while a wave of lower frequency has a longer wavelength.
(iv) Wave number: This is the reciprocal of wavelength. The number of wavelengths per unit of length covered is called wave number of wave. It is denoted by the symbol v (nu bar) or the symbol k. Its units are cm–1 or m-1.
Thus, wave number = 1 / λ
(v) Amplitude: The height of the crest or depth of the trough of a wave is called amplitude of the wave. It is denoted by the letter ‘a’ or ‘A’. It determines the intensity of the radiation.
vi) Time period: Time taken by the wave for one complete cycle or vibration is called time period. It is denoted by T and its unit is second per cycle.
Mathematically, Time period (T) = 1/v (frequency)
Solved Examples on Wave Nature of Electromagnetic Radiation
Let’s take some solved examples based on the wave nature of electromagnetic radiation.
Example 1: Calculate its frequency and wave number if the wavelength of a violet light is 400 nm.
Solution:
We know that frequency, v = c / λ
Velocity, c = 3.0 × 10 8 ms–1 (given)
Wavelength, λ = 400 nm = 400 × 10–9 m
Frequency of the wave v = c / λ = 3 × 10 ms-1 / 400 × 10-9 m
Thus, frequency of wave v = 7.5 × 1014 sec–1 (Ans)
Wave number = 1 / λ = 1 / 400 × 10-9 m = 25 × 105 m–1 (Ans)
Example 2: Calculate the wavelength of the light in nanometers if the frequency of strong yellow line in the spectrum of sodium is 5.09 × 1014 sec–1.
Solution:
We know that wavelength, λ = c / v
Here, velocity c = 3.0 × 108 msec–1 and ν = 5.09 × 1014 sec–1 (given)
Wavelength, λ = 3.0 × 108 msec–1 / 5.09 × 1014 sec–1 = 589 × 10 –9 m = 589 nm (Ans)
