The wavelength of photons tells us about their energy. So in this article, we will look at what is the wavelength of photons and how to find it. Let us begin.
Photons travel through electromagnetic waves. As the photon is ultimately a part of the electromagnetic wave, its wavelength will be the same as the electromagnetic wave. If the energy and frequency of a photon are known, then from that, one can easily find the wavelength of the photon.
Before we get into the wavelength of a photon, let’s have a look at what a photon is.
Photon:
As the energy that is contained by photons is not divisible, they are often described as energy packets. Maxwell has described photons as electric fields which are traveling through space. Or, to put it another way, photon energy is stored in the form of an oscillating electric field that can oscillate at any frequency. Thus a quantum of electromagnetic radiation or energy is called a photon.
Photons are particles that have neither a charge nor a mass. As a result, they are able to travel at the speed of light. The speed of the electric field can decide the speed of the photons in free space. The emission of photons is possible by means of the action of the charged particles and some other methods like radioactive decay.
What is the wavelength of photon?
The properties of photons are the same as those of electromagnetic waves. As a result, each photon is associated with its unique frequency and wavelength.
Photons travel in waves, as though each one is riding a roller coaster that only uses the same track repeatedly. The wavelength of a photon wave is the length of the wave, or more precisely, the distance between two consecutive points of the same phase of the wave.
Three different wavelengths are shown in the diagram below. Although photons do not have color, they will correspond to the light of that particular color.
How to find wavelength of a photon?
The length of an electric field wave, or a photon wave, is the wavelength of a photon.
To determine the wavelength of a photon, either its energy or frequency is used. As a result, if any of them are known, the wavelength of a photon can be found easily.
Let’s look at how to find wavelength of a photon using frequency and energy.
How to find wavelength of a photon with frequency?
The frequency and the wavelength of a photon are related to each other.
The length of the photon wave gives the wavelength of the photon wave. While the number of photon wavelengths that propagates every second gives us the frequency of photon waves. As a result, if a photon’s wavelength is short, its frequency will be high, and its frequency will be low if its wavelength is long.
As one increases while the other decreases, we can say that they have an inverse relationship. Let us derive a mathematical equation that reflects the link between photon frequency and wavelength.
Several quantities such as wavelength, period, frequency, and so on can be used to describe a wave. As we know, the frequency of a photon wave determines the number of photon waves that propagate each second. As a result, the frequency of a photon wave can be calculated as follows:
……….(1)
Where f is the frequency of the photon wave, and T is the period of the photon wave, i.e., the time it takes for the photon wave to complete one cycle.
After one period, every wave point returns to the same value. This happens because in a wave during one period, one oscillation occurs, and each oscillation travels a distance of one wavelength in that time.
The distance traveled by any wave in a unit of time determines its speed. But as the wave is traveling with the speed of light, thus we denote it with the letter c, and it can be given by:
……….(2)
From equations (1) and (2), we can write:
c = ????f ……….(3)
Thus, the wavelength of the photon is given by:
……….(4)
Because the speed of light c is constant and has a value of 3 X 108 m/s, we may deduce from the above equation that the wavelength of a photon is inversely proportional to its frequency.
How to calculate wavelength of a photon given energy?
The frequency of a photon relates to both its energy and wavelength. As a result, the photon’s wavelength is also connected to its energy.
The photon wave’s wavelength contains information about its energy. A shorter wavelength photon wave will have a higher frequency and consequently higher energy. Similarly, a photon wave with a longer wavelength will have a lower frequency and thus less energy.
Also, in this case, a longer wavelength corresponds to lower wave energy, whereas a shorter wavelength corresponds to higher wave energy. As a result, we can state that the wavelength of the photon wave and its energy are inversely proportional. In terms of an equation, let’s look at the relationship between energy and wavelength of the photon wave.
According to the great scientist Max Plank, light is composed of discrete packets of energy known as quanta of light, which are also known as photons. The energy of light can only have discrete values. Plank further said that energy is given by the product of photon frequency and a constant known as Plank’s constant. We can express it mathematically as follows:
E = hf ……….(5)
Where h = Plank’s constant (6.626 X 10-34 J s)
When we compare equations (4) and (5), we get the following expression for energy:
……….(6)
Rearranging Plank’s equation, the wavelength of a photon in terms of energy is given by:
……….(7)
Thus, if the energy of a photon or light wave is known, the wavelength of the photon can be determined using Plank’s equation.
Some problems of finding the wavelength of the photon using frequency and energy:
Problem: What is the wavelength of a light wave with a frequency of 7 X 1014 Hz?
Given parameters:
Frequency of photon f =7 X 1014 Hz
Speed of light c = 3 X 108 m/s
To Find:
Wavelength of photon ???? = ?
Solution:
???? = c / f
???? = 3 X 108 / 7 X 1014
∴ ???? = 0.428 X 10-6 m
∴ ???? = 428 nm
As a result, a photon with a frequency of 7 X 1014 Hz has a wavelength of 428 nm.
Problem: What wavelength will a photon have if its energy is4 X 10-15 J?
Given parameters:
Energy of photon E = 4 X 10-15 J
Plank’s constant h = 6.626 x 10-34 Js
Speed of light c = 3 X 108 m/s
To Find:
Wavelength of photon ???? = ?
Solution:
???? = hc/ E
???? = 6.626 X 10-34 X 3 X 108 / 4 X 10-15
∴ ???? = 5 X 10-11 m
∴ ???? = 500 nm
As a result, a photon with an energy of 4 X 10-15 J has a wavelength of 500 nm.
Problem: If the energy of a photon is 2.19 × 1011 ev, determine the wavelength of that photon.
Given parameters:
Energy of photon E = 2.19 × 1011 ev
∴ E = 2.19 × 1011 X 1.6 X 10-19
∴ E = 3.05 × 10-8 J =350 X 10-10 J
Plank’s constant h = 6.626 x 10-34 Js
Speed of light c = 3 X 108 m/s
To Find:
Wavelength of photon ???? = ?
Solution:
???? = hc/ E
???? = 6.626 X 10-34 X 3 X 108 / 350 X 10-10
∴ ???? = 0.056 X 10-16 m
As a result, a photon with an energy of 2.19 × 1011 ev has a wavelength of 0.056 X 10-16 m.
Also Read:
- Amplitude of a wave example
- How to harness mechanical energy in wave power generation
- Why is light considered both a wave and a particle in quantum mechanics
- How to find energy from wavelength
- Amplitude of a wave
- Wave interference examples
- How to find amplitude of transverse wave
- Electromagnetic waves types
- Why does light exhibit both wave and particle characteristics
- Effect of wavelength on refraction
I am Alpa Rajai, Completed my Masters in science with specialization in Physics. I am very enthusiastic about Writing about my understanding towards Advanced science. I assure that my words and methods will help readers to understand their doubts and clear what they are looking for. Apart from Physics, I am a trained Kathak Dancer and also I write my feeling in the form of poetry sometimes. I keep on updating myself in Physics and whatever I understand I simplify the same and keep it straight to the point so that it deliver clearly to the readers.