## Light Energy - Electromagnetic waves and EM spectrum, Practice problems, FAQs

When we talk about nature, many pictures come into our minds. We have seen many creatures, mountains, oceans, stars, satellites, etc. But how we can see them or how we can identify them. So the answer is “light”. It is light due to which we can see the things around us. When the light strikes on any body it absorbs the colors reflecting the certain colors or color, when the light containing that reflecting color reaches to our eyes we can see that object with the respective color. This light also contains energy which is being discussed in this topic is known as the light energy.

Table of content

• Electromagnetic waves and EM spectrum
• Light energy and production
• Photon: Definition, properties, count, energy, and flux
• Light and intensity of light
• Types of light energy
• Uses of light energy
• Practice problems
• FAQs

Electromagnetic waves and EM spectrum

Electromagnetic waves are the waves that are produced due to the interaction of the oscillating electric field and the oscillating magnetic field. In this wave, the electric field and the magnetic field are perpendicular to each other and vary sinusoidally. EM wave does not require any medium to propagate and in vacuum, it travels with a speed of 3108 m/s.

Electromagnetic radiation is the form of energy that is produced due to the interaction of oscillating electric fields and magnetic fields. This electromagnetic radiation has a wide range of frequencies and wavelengths in which the frequency is in decreasing order and the wavelength is in the increasing order and this range is known as the electromagnetic spectrum. The EM spectrum is shown in figure below,

Light and intensity of light

Light is the bunch of different wavelengths of electromagnetic radiation that are visible or invisible (Like gamma rays, X-rays, etc) to the human eye. The light that can be seen by the human eye in the form of colour is known as visible light.

Intensity of light: It is the amount of radiation energy falling on a unit area perpendicular to it over a unit time interval.

Mathematically it is represented as,

A= Area on which the radiation is falling

t= Time interval

n= Number of photons incident on area per unit time

Light energy and production

Light energy is the type of kinetic energy related to the electromagnetic radiation and it is generated in the form of electromagnetic radiation when an object is heated up. The object can be a natural source like the sun or it can be a human made device like lasers, bulbs etc. Visible light is one of the ranges in the electromagnetic spectrum that can be seen by the human eye and depending on the reflecting nature of the object on which the light is imparting, we can see that object.

Photons, which are tiny energy packets, are present in light. Photons are created when the atoms of an object become heated; this is how photons are created. The heat excites the electrons, which leads to them producing more energy. The energy is released as a photon, and as the substance heats up, more photons are emitted.

As it moves, light energy adopts the form of a wave. No matter what, it is necessary to transport light energy in order to go. This is the reason why light energy can travel into space where there is no air, but sound waves cannot because they need a medium like solids, liquids, or gases to travel. Light energy moves more quickly than any other kind of energy (with the speed of light).

Photon: Definition, properties, count, energy, and flux

Photons are the packets of electromagnetic energy and have particle-like behavior. Earlier it was known that the light has a wave-like nature but through the photoelectric effect, it was observed that the light consists of discrete bundles of energy called photons.

Properties of photon:

1. Rest mass of photon is zero.
2. Energy and momentum of photon is always conserved.
3. Photons travel with the speed of light.
4. Photons do not carry any charge.

Photon energy and momentum:

Energy of a photon is given by,

𝐸=ℎ𝑣

Where, h is Planck constant and 𝑣 is frequency

And the momentum of a photon is given by,

$p=\frac{E}{c}=\frac{h}{\lambda }$

Where, 𝜆= wavelength, c= speed of light

Photon count and flux:

Photon count is the number of photons emitted per second by the energy source.

$n=\frac{P}{E}=\frac{P\lambda }{hc}$

Where, P= Power of source $=\frac{E}{t}$

Photon flux is defined as the number of photons incident perpendicularly on a surface per second per unit area.

$\varphi =\frac{n}{A}=\frac{I\lambda }{hc}$

Types of light energy

1. Visible light energy: The form of kinetic energy of electromagnetic radiation which is contained in the visible light is known as the visible light energy. (Bulbs, flashlights)
2. Infrared light energy: The form of kinetic energy of electromagnetic radiation which is produced in the infrared radiation is known as the infrared light energy. (TV remote of the TV)
3. X-rays and ultraviolet light; The form of kinetic energy of electromagnetic radiation which is produced during X-rays and ultraviolet radiation is known as the infrared light energy. (X-rays used for detecting the fractures in the bones)

Uses of light energy

1. Vision: Because many living creatures have eyes, which would be worthless without light, they can see the world around them. As the light strikes our eyes, an image is produced, and the brain receives this information. Light energy thus enabled us to observe our surroundings.
2. Colours: The sun makes it possible for all of the vibrant colours that make up the world. Each of the light's spectra, including VIBGYOR, has its own distinct colour.
3. Food and health: All living things can only produce nourishment when there is light. All living things rely on light for both their energy and nourishment, with the exception of a few chemotrophic species like bacteria. Also Vitamin-D, which is provided by sunlight and aids in strengthening bones.

## Practice problems

Q1. A 180 W light bulb is emitting light with the efficiency of about 4%. Calculate the number of photons emitted per second from the bulb if the wavelength of the emitting light is 600 nm.

().

A. Given, efficiency of the bulb =4%

Then the emitted energy per second will be,

Again the energy emitted is given by,

$E=h\nu ×n=n\frac{hc}{\lambda }$

Then the no. of photons that are emitting per second will be,

$⇒n=\frac{E\lambda }{hc}$

$⇒n=\frac{7.2×600×{10}^{-9}}{6.63×{10}^{-34}×3×{10}^{8}}=2.2×{10}^{19}$

Q2. The surface of the earth receives$1.5×{10}^{3}\frac{W}{{m}^{2}}$ of sunlight when the sun is overhead to it. Assume that the light is monochromatic with average wavelength 500 nm and no light is absorbed in between the sun and the earth’s surface then find the number of photons falling per m2 per second on the earth’s surface directly below the sun. The distance between the Earth and the Sun is measured as .

Answer. Given, intensity of sunlight reaching to the Earth’s surface, $I=1.5×{10}^{3}\frac{W}{{m}^{2}}$

Distance between the sun and the earth

Wavelength of the monochromatic light

Then the intensity of the light is given by,

$I=n\frac{hc}{A\lambda }$

Q3. With the help of a graph, explain the variation of Energy and Momentum of a photon.

A. We know the energy that exists in a photon is given by,

Where p is the momentum, and c is the speed of light in vacuum

The equation (i) is similar to, y = mx

Now if we take E on y-axis and p on the x-axis then the graph will be drawn as shown below,

Hence the variation of Energy and Momentum of a photon is linear and the slope of the straight line will be speed of light in vacuum (c).

Q4. Find the force experienced by the a plane mirror due to incidence of a parallel beam of monochromatic light of wavelength 600 𝑛𝑚. The angle of the incidence of the beam is 30° and 1.2×1019 number of photons are imparting on the mirror per second.

Answer. Given, number of photons striking per second, $n=1.2×{10}^{19}$

Wavelength of the monochromatic light,

Angle of incidence of the beam, $\theta =30°$

Where, I= Intensity of the light

c= Speed of light

In the equation (i), the intensity of light is given by,

$I=n\frac{hc}{\lambda Acos\theta }$

Then equation (i) will become,

Since the the direction of force is perpendicular to the plane mirror then the force exerted by the light beam on the mirror is,

F=PA

From equation (ii)

$F=\frac{2nh}{\lambda }cos\theta$

## FAQs

Q1. Define light energy?
The kind of energy produced due to electromagnetic radiation is known as light energy. It is produced when an object is heated up and by this, the photons and electrons are released.

Q2. Where does the visible spectrum of light lie in the electromagnetic spectrum?