What is the relationship between mass and energy according to E=MC^2?

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Discussion Overview

The discussion revolves around the relationship between mass and energy as described by the equation E=mc². Participants explore its applicability to different types of matter, including point particles and atomic nuclei, and examine the implications of nuclear fission and fusion in this context.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether E=mc² applies to point particles like electrons or is limited to atomic nuclei held together by the strong force.
  • Another participant asserts that E=mc² pertains to the energy of any mass at rest and can be used to calculate energy from particle annihilation.
  • A participant raises a concern about the energy released during uranium-235 fission, suggesting that the mass-energy equivalence does not apply straightforwardly since most of the mass remains after fission.
  • Further clarification is provided that uranium fission releases only a small fraction of the total mass-energy of the uranium atom.
  • A participant expresses confusion about the energy dynamics of nuclear fission versus fusion, questioning why fusion, being the opposite of fission, does not consume energy.
  • Another participant explains that fusion tends to release energy for light isotopes while fission typically requires energy input for heavy isotopes, noting the significance of the binding energy curve.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of E=mc² to various types of mass and the energy dynamics of nuclear processes. There is no clear consensus on these points, and the discussion remains unresolved.

Contextual Notes

Participants reference the complexities of mass-energy conversion in nuclear reactions, including the nuances of binding energy and the specific conditions under which fission and fusion occur. Some assumptions about the nature of particles and energy release are not fully explored.

jaydnul
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Quick question... does that equation refer to any type of matter, like a point particle? Or does it refer to atoms that have nuclei that are attached by the strong force? Lemme put it another way. Take a point particle, an electron... now if you found a way to convert that single electron into energy, would e=mc^2 calculate how much energy that would be? Or does e=mc^2 just refer to the energy inside an atomic nucleus aka the strong force?
 
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That equation concerns energy of any mass at rest.
If it has got rest mass and is not moving, then it's got that energy.
You can use it to calculate the energy released from the annihilation of an electron with a positron.

Also, I'm pretty sure the "point particle" status of an electron is just an approximation, not actual physical reality.
 
So when u-235 is split the energy released isn't equal to (mass of uranium)*(c^2) right? Because a majority of that mass is still there just in two different pieces.
 
lundyjb said:
So when u-235 is split the energy released isn't equal to (mass of uranium)*(c^2) right? Because a majority of that mass is still there just in two different pieces.

Yes. Uranium fission only releases a very small fraction of the total mass-energy of the uranium atom. The U-235 bomb that destroyed Hiroshima in 1945 contained about 50 kilograms of U-235, of which a bit less than one kilogram fissioned before the bomb blew apart. The explosion released maybe 5x1013 Joules of energy, meaning that about .5 grams of mass was converted to energy.

(These are round numbers because I'm doing the calculations in my head. Google will find you more precise numbers, but I've got the ranges of sizes about right).
 
ahh very interesting. thanks!

Also something that has me a little confused is this: since nuclear fission releases energy, it seems that nuclear fusion should consume energy given that its the opposite of fission. But that's not the case because the sun runs on nuclear fusion. Why is that?
 
For light isotopes, fusion tends to release energy and fission tends to require energy input. For heavy isotopes, it's the other way around. The "turnover point" is around iron. Google for "binding energy curve" and you'll probably turn up explanations.
 

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