# Does Energy Have Mass: Why, When, How, Why Not (13 Simple Facts)

Every mass possesses energy whether the mass is in motion or at rest. But does energy have mass? Let us try to answer this.

If energy has mass then what is the point of talking about the energy of the massless photon, and if your answer is no then why do all the particles moving with the speed of light possesses the mass which is equal to $m=\frac{E}{c^2}$.

## Do all energy have mass?

The energy is related to the mass by the relation $E=mc^2$, hence greater the mass the more is energy stored.

This mass is converted into energy when the particle is in motion. The particle moving with the energy does possess mass if the speed of the particle is equal to the speed of light.

## What is the energy of the object having a mass of 52kg moving with respect to the velocity of light?

Given: m =52kg

$c=3\times 10^8 m/s$

We have,

$E=mc^2$

$=52\times (3\times 10^8)^2$

$=52\times 9\times 10^16$

$=468\times 10^16J$

The energy that the object possesses is $468\times 10^16\ Joules$.

## Which energy has mass?

If the mass and momentum of the matter are conserved while doing some work using the energy then the energy has mass.

The energy will be converted into another form of energy, for example, the mechanical energy will be converted into the kinetic energy to thermal energy due to abrasion and friction, then, the kinetic and thermal energy will radiate the energized particle that possesses mass and conserve the total energy.

Even the sound energy travels producing the vibrational energy along the path oscillating the molecules in the medium back and forth. This vibrating molecule that carries the sound waves does have mass.

## Which energy does not have mass?

If energy is directly related to mass then how it can be possible to have energy that has no mass.

All the energies do behave like a mass, as the energy of the mass increases the mass has to be also increased. The energy radiated from far distances does not have mass because it loses the energy by emitting the radiation as it travels a long distance.

## When energy does not have mass?

The energy is directly proportional to the mass of the matter and the energy is stored with every particle constituting it.

Accordingly, the energy can be converted to mass, and mass into energy. From the special theory of relativity, it is depicted that any particle traveling at the speed of light with kinetic and radiant energy has to be massless.

## Where energy does not have mass?

From Einstein’s equation of relativity showing the relation between the mass and energy, if m=0 then energy has to be zero.

But it is noticed that the speed and the energy of the small particles like photons, neutrons, and electrons, travel almost at a speed of light which are all nearly the massless particle but do possess the energy, and hence we can conclude that it is possible to have energy without a mass.

## How does energy have mass?

If the particle is at rest then the total energy possessed by the particle is equal to $m_0c^2$.

The energy is directly dependent on the mass of the particle hence if the energy of the particle is more, then the energy stored by the particle will also be more.

The mass of a vehicle at rest is supposed 1 imperial ton and has chemical and mechanical energy stored with it, this will produce kinetic energy once the vehicle starts accelerating and now the mass of the vehicle will be slightly reduced as the mass of the fuel in the vehicle is converted into the energy.

On contrary, this mass will be added to the kinetic energy of the vehicle and hence the total mass will be the sum of the mass resulting in gaining the kinetic energy too.

## What is the mass of the particle moving with the velocity of light having the energy of 300J?

Given: E =300J

$c=3\times 10^8 m/s$

We have,

$m=\frac{E}{c^2}$

$=\frac{300}{(3\times 10^8)^2}$

$=\frac{300}{9\times 10^{16}}$

$=3.33\times 10^{-15}kg$

The mass of the particle is $3.33\times 10^{-15}kg$.

## Does light have mass?

Light is a radiant form of energy carried by the massless particles because the speed of the particle carrying the light is equal to c.

The total energy of the particle is the energy of the mass and the momentum of the particle that is $E^2=p^2c^2+m^2c^4$, but in the case of light, m=0 hence the energy of the light is $E=pc$.

The light energy shows momentum and collision, and gets all the energy from its momentum and moves with the great energy in proportional to the momentum.

## Does photon have mass?

The photon is a small quanta of light and shows both natures of behavior as a wave and point particle.

The photon possesses electromagnetic energy and travels with the speed of light hence it is predicted that the photon has to be massless based on the special theory of relativity.

## Why do photons have no mass?

The photon has energy and momentum but yet it is massless.

The energy with which the photon travels is equal to E=pc because its mass is zero as it travels with a speed of light and its momentum is conserved. The photon cannot be stopped.

For a particle traveling with mass and momentum, the total energy by relativity is given as

$E=\sqrt{p^2c^2+m^2c^4}$

For a particle at rest, momentum will be zero i.e. p=0 then

$E=\sqrt{m^2c^4}=mc^2$

In relativistic theory, the total energy with which the photon is moving is equal to

$E=\frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}$

Rearranging this equation we can write an equation for mass as

$m=\frac{E}{c^2}{\sqrt{1-\frac{v^2}{c^2}}}$

The photon travels with a speed of light then v=c.

$m=\frac{E}{c^2}{\sqrt{1-\frac{c^2}{c^2}}}$

$m=\frac{E}{c^2}{\sqrt{1-1}}$

$m=\frac{E}{c^2}\times 0$

$m= 0$

The mass of the photon is found to be zero since the speed of the photon is equal to c.

## What is the momentum of the photon having a wavelength of 550 nm?

We know that $\lambda =550 nm$

$h=6.62\times 10^{-34}J.s$

$c=3\times 10^{8}m/s$

The energy of the photon moving with a wavelength of 550 nm is

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

The energy of the photon since its momentum is conserved is

$E=pc$

Hence the momentum of the photon is

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

Substituting the term of E in this equation,

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

This is the equation of the momentum of the photon. Hence inserting the values

$=\frac{6.62\times 10^{-34}}{550\times 10^{-9}}$

$=0.012\times 10^{-25}$

$=1.2\times 10^{-27}$

The momentum of the photon is $1.2\times 10^{-27}kg.m/s$.

## Can energy lose mass?

The mass is not lost but it is transformed into energy.

The object at rest has the actual mass ‘m’ and this mass is converted into energy thus reducing the total mass of the object. If the object receives an additional amount of energy then this is converted into the mass increasing the total mass of the object.

You must have noticed while riding on a Ferris wheel. As the wheel is accelerating above the ground from the bottom, your body is actually gaining the potential energy which is the additional source of energy and hence you feel the heaviness of body mass. The potential energy gained is converted into the mass and the total mass increases more than the actual.

But while accelerating down, this potential energy is converted into kinetic energy and the acceleration is also in the direction of gravitational pull hence your body feels light weighted. The mass is converted into energy while returning down to the ground and hence the weight is slightly reduced.

## How can energy lose mass?

The mass is converted into the energy as the mass and energy are correlated and this relation is given by the formula $E=mc^2$.

If the energy acquired by the mass is greater, then it will move at high speed and thus the mass of the particle will be greater. As the particle is traveling from a far distance it radiates the energy and thus reducing its mass.

If this particle comes to a rest position then this energy will be converted back into the potential energy. Every mass of the object possesses some amount of energy that can be converted into different forms of energy or store the energy. If a large amount of mass is transformed then a huge amount of energy will be produced by the matter.

## When can energy lose mass?

The energy is converted into mass when the particle is in motion or doing some work utilizing its potential energy.

The mass of the particle or an object in motion has a mass equal to $m=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}$ in relativistic, where m is a mass of the particle in motion and $m_0$ is its rest mass.

## What is the mass of the particle traveling with a speed of 0.3c if the rest mass of the particle $1.5\times 10^{-27}kg$?

Given: $m_0= 1.5\times 10^{-27}kg$

v =0.3c

We have,

$m=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}$

$=\frac{1.5\times 10^{-27}}{\sqrt{1-\frac{(0.3c)^2}{c^2}}}$

$=\frac{1.5\times 10^{-27}}{\sqrt{1-\frac{0.09c^2}{c^2}}}$

$=\frac{1.5\times 10^{-27}}{\sqrt{1-0.09}}$

$=\frac{1.5\times 10^{-27}}{\sqrt{0.91}}$

$=\frac{1.5\times 10^{-27}}\times 0.95$

$=1.58\times 10^{-27} kg$

Hence we can see that the mass of the particle has increased slightly than the actual amount of $=0.08\times 10^{-27}kg$ when it is in motion.

## Where can energy lose mass?

The energy loses mass if the mass is converted into energy and given away in the process.

The energy can lose the mass in the combustion of fuels, in a nuclear reaction as the nuclear binding energy is converted into thermal energy and emitted out, in the decomposition process. Even the sun losses its mass by producing heat and light which is emitted in the form of electromagnetic radiation.

## How mass is different from velocity?

The mass is independent of the kinetic energy of the object while the velocity is dependent on energy.

The mass is the quantity of particles possessed by the object while the velocity of the object defines the energy acquired by the object.

## Can energy be really converted into mass?

The energy and mass are interdependent hence if mass can be converted into energy then so is the energy to mass.

The energy can be converted to mass but a huge amount of energy is required to do so. You must have found the increase in the mass of the object when it is moving with great energy and speed.

#### Summary

The energy has a mass and it can be massless also. The energy that a particle possesses is due to its mass and momentum. For the massless particle, the energy that it gains is from the momentum and the speed of such particles which are massless moves with a speed equal to light particles.

AKSHITA MAPARI

Hi, I’m Akshita Mapari. I have done M.Sc. in Physics. I have worked on projects like Numerical modeling of winds and waves during cyclone, Physics of toys and mechanized thrill machines in amusement park based on Classical Mechanics. I have pursued a course on Arduino and have accomplished some mini projects on Arduino UNO. I always like to explore new zones in the field of science. I personally believe that learning is more enthusiastic when learnt with creativity. Apart from this, I like to read, travel, strumming on guitar, identifying rocks and strata, photography and playing chess. Connect me on LinkedIn - linkedin.com/in/akshita-mapari-b38a68122