# Matter to Energy: Kinetic + Rest Mass?

• Shark 774
In summary, the law of conservation of energy and momentum applies to the decay of a moving particle, where the total energy and momentum of the decay products is equal to the total energy and momentum of the original particle. This applies for both non-relativistic and relativistic speeds.
Shark 774
If a particle is moving at some particular speed and then suddenly decays, is the energy released equal to the rest mass of the particle plus the kinetic energy it had before decay, or simply its rest mass??

Thanks.

It has to equal both the rest energy and the kinetic energy that the original particle had.

The "Law of Conservation of Energy" must be applied here.

Energy Before Decay = Energy After Decay

Sup_Principia said:
The "Law of Conservation of Energy" must be applied here.

Energy Before Decay = Energy After Decay

Correct me if am wrong but is it correct. i thought the merely acceleration of the object should account for a change in mass hence relativistic energy is considered. Shouldn't it be the relativistic energy instead of the rest energy..

Ikoro said:
Correct me if am wrong but is it correct. i thought the merely acceleration of the object should account for a change in mass hence relativistic energy is considered. Shouldn't it be the relativistic energy instead of the rest energy..

In the original post (OP) there was no mention of how fast the "Mass" particle was moving.

Shark 774 said:
If a particle is moving at some particular speed and then suddenly decays, is the energy released equal to the rest mass of the particle plus the kinetic energy it had before decay, or simply its rest mass??

I assumed non-relativistic speed because it was not mentioned! In Shark's question the "Moving Mass" particle decays. He does not say whether the decay object is a "Photon" or another separate "Mass" unit.

In either case the Conservation of energy applies.

Inertial Mass --- Inertial Mass
Energy Before Decay = Energy After Decay

$$\frac{1}{2} m_{Net}{v^2_{Original}} = \frac{1}{2} m_{New}{v^2_{New}} + \frac{1}{2} m_{Decay}{v^2_{Decay}}$$

Inertial Mass --- Photon
Energy Before Decay = Energy After Decay

$$\frac{1}{2} m_{Net}{v^2_{Original}} = \frac{1}{2} m_{New}{v^2_{New}} + h_{Planck}f_{frequency}$$

If the above does not address the post, then either Ikoro or Shark needs to be a bit clearer!

Sup_Principia said:
Inertial Mass --- Photon
Energy Before Decay = Energy After Decay

$$\frac{1}{2} m_{Net}{v^2_{Original}} = \frac{1}{2} m_{New}{v^2_{New}} + h_{Planck}f_{frequency}$$

If the above does not address the post, then either Ikoro or Shark needs to be a bit clearer!

Being a relativity forum, relativistic equations rather than Newtonian equations may be more appropriate so:

Inertial Mass --- Photon
Total Energy Before Decay = Total Energy After Decay

$$\frac{M c^2}{\sqrt{1-v^2/c^2}} = \frac{M_{final} c^2}{\sqrt{1-v_{final}^2/c^2}} + hf$$

Just for info:

M is the rest mass and the original kinetic energy is:

$$\frac{M c^2}{\sqrt{1-v^2/c^2}} - M c^2$$

Last edited:
yuiop said:
Being a relativity forum, relativistic equations rather than Newtonian equations may be more appropriate so:

Inertial Mass --- Photon
Total Energy Before Decay = Total Energy After Decay

$$\frac{M c^2}{\sqrt{1-v^2/c^2}} = \frac{M_{final} c^2}{\sqrt{1-v_{final}^2/c^2}} + hf$$

Just for info:

M is the rest mass and the original kinetic energy is:

$$\frac{M c^2}{\sqrt{1-v^2/c^2}} - M c^2$$

Thanks for your response, that clears it up. You're right, this is a relativity forum and hence people may need to use a little more common sense, rather than others needing to be clearer.

yuiop said:
Being a relativity forum, relativistic equations rather than Newtonian equations may be more appropriate so:

Shark 774 said:
Thanks for your response, that clears it up. You're right, this is a relativity forum and hence people may need to use a little more common sense, rather than others needing to be clearer.

First and foremost; Physics is an exact science, and words do matter. This is like saying, "Is that a soda?" When you really intended to say "Is that a "Coke 'a' Cola!"

Second; one of the main tenents of "Special Relativity" is the knowledge of the photon and its speed of light motion relative to matter. And this was why I added both equations, one that was relativistic at low speeds, and one that involved classical relativity.

Third; I answered you question, in a way that was to reveal how much "non-sense" was in your question. Or said in a nice way, to reveal that your question was not posed as clear as it should have been!

We are not in the 1800's anymore, in the 21st Century there is so much physics we

yuiop said:
Inertial Mass --- Photon
Total Energy Before Decay = Total Energy After Decay

$$\frac{M c^2}{\sqrt{1-v^2/c^2}} = \frac{M_{final} c^2}{\sqrt{1-v_{final}^2/c^2}} + hf$$

Just for info:

M is the rest mass and the original kinetic energy is:

$$\frac{M c^2}{\sqrt{1-v^2/c^2}} - M c^2$$

Maybe yuiop, Shark are not use to being specific; but the above equation is a bit more special relativity specific, using the following equations.

Rest Mass
$$m_{Net_0}$$

Relativistic Mass Before Decay
$$\frac{m_{Net_0}}{\sqrt{1-v^2_{Initial}/c^2_{Light}}}$$

Mass due to relativistic motion that is added to the Rest Mass Before Decay
$$\Delta m_{Motion} = \frac{m_{Net_0}}{\sqrt{1-v^2_{Initial}/c^2_{Light}}} - m_{Net_0}$$

Relativistic Doppler Frequency Observed
$$f_{Observed} = f_{Souce} \sqrt{\frac{1 - \frac{v_{final}}{c_{Light}}}{1 + \frac{v_{final}}{c_{Light}}}}$$

Inertial Mass --- Photon
Total Energy Before Decay = Total Energy After Decay

$$\frac{m_{Net_0}c^2_{Light}}{\sqrt{1-v^2_{Initial}/c^2_{Light}}} = \frac{m_{Net_0}c^2_{Light}}{\sqrt{1-v^2_{Final}/c^2_{Light}}} + h_{Planck}f_{Observed}$$

$$m_{Net_0}c^2_{Light} + \Delta m_{Motion}c^2_{Light} = \frac{m_{Net_0}c^2_{Light}}{\sqrt{1-v^2_{Final}/c^2_{Light}}} + (h_{Planck}f_{Souce}) \sqrt{\frac{1 - \frac{v_{final}}{c_{Light}}}{1 + \frac{v_{final}}{c_{Light}}}}$$

Hopefully this is relativistic enough for you!

Shark 774 said:
If a particle is moving at some particular speed and then suddenly decays, is the energy released equal to the rest mass of the particle plus the kinetic energy it had before decay, or simply its rest mass??
The total energy (mass energy + kinetic energy) of the decay products is equal to the total energy of the reactants. Total energy is conserved. The total momentum is also conserved.

## 1. What is the concept of matter to energy conversion?

The concept of matter to energy conversion is based on Einstein's famous equation, E=mc², which states that matter and energy are interchangeable. This means that matter can be converted into energy and vice versa.

## 2. How does the conversion of matter to energy occur?

The conversion of matter to energy can occur through various processes, such as nuclear reactions, chemical reactions, and particle collisions. These processes involve breaking down the atomic bonds within matter, releasing energy in the form of radiation or kinetic energy.

## 3. What is the role of kinetic and rest mass in matter to energy conversion?

Kinetic energy refers to the energy of motion, while rest mass is the mass of an object at rest. In matter to energy conversion, both kinetic and rest mass are important as they contribute to the total energy released. The faster the particles move, the higher the kinetic energy and the more energy can be converted from matter to energy.

## 4. Can all types of matter be converted into energy?

According to the law of conservation of mass and energy, matter cannot be created or destroyed, it can only be converted into different forms. Therefore, all types of matter have the potential to be converted into energy, but the amount of energy released may vary depending on the type of matter and the conversion process.

## 5. What are some real-life applications of matter to energy conversion?

Matter to energy conversion has many practical applications, such as in nuclear power plants, where nuclear reactions are used to generate electricity. It is also utilized in medical imaging technologies, such as PET scans, which use the conversion of matter to energy to produce images of the body's internal structures. Additionally, matter to energy conversion is used in the production of nuclear weapons and in the development of new energy sources, such as fusion energy.

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