Why does all the excess BE go to the radiated particle?

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Discussion Overview

The discussion revolves around the energy loss during alpha decay, specifically questioning why the excess binding energy (BE) appears to be entirely transferred to the emitted alpha particle rather than being shared with the resulting daughter nucleus. Participants explore the implications of energy and momentum conservation in this context.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant notes that textbooks state a nucleus loses energy by radiation but questions why all excess BE is attributed to the alpha particle, suggesting a need to consider energy given to the new nucleus.
  • Another participant calculates that the kinetic energy of the alpha particle is approximately 55.5 times greater than that of the radon nucleus, implying that the recoil of the daughter nucleus can be neglected for practical purposes.
  • A different participant agrees that the daughter nucleus must recoil in the opposite direction to conserve momentum, emphasizing that both energy and momentum conservation are essential in this scenario.
  • Several participants express a desire for clearer explanations, with one requesting a direct address of the original question without delving into complex details.
  • One participant encourages others to ask specific questions to clarify misunderstandings and highlights the importance of distinguishing between mathematics and physics in understanding the concepts.

Areas of Agreement / Disagreement

Participants generally agree on the principles of conservation of momentum and energy but have differing views on the implications of these principles regarding the distribution of energy during alpha decay. The discussion remains unresolved as participants seek clarity on specific aspects of the topic.

Contextual Notes

Some participants express confusion over the mathematical aspects of the discussion, indicating a potential gap in understanding the relationship between the physics concepts and their mathematical representations.

kenshi64
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Well all textbooks probably state something like this 'A Nucleus loses energy by radiation'

I'm cool with that statement except the fact that all the excess BE or energy is lost only to the eg.alpha particle! and no mention of some being given to the new nucleus!

Look at this for example:
Mass Radium=226.0254u
Mass Radon=222.0176u
Mass Helium(Alpha)=4.002602u
Change in mass=0.005198u
Energy equivalent=4.84MeV

Note: Energy of alpha=5MeV
Resemblance of 4.84MeV to 5MeV-Uncanny
So this is going to say that the lost BE is all given to the alpha, WHY?
(or am I supposed to consider 5-4.84 for the energy given to the new nucleus)
 
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Solving the conservation of momentum and energy in this case tells you that the kinetic energy of the alpha particle will be approx 55.5 times more than that of the radon nucleus.

So I guess that to a good approximation, you can ignore the recoil of the daughter nucleus.
 
Agreed Simon_Tyler, Kenshi64 the daughter nucleus MUST recoil in the opposite direction to the alpha to conserve momentum. It's not just energy which must be conserved.

PS Even if the radiation is a gamma (so no rest mass) it still has momentum given by E/c
where E is its energy and c as usual is the speed of light
 
Kenshi64 see attached for all the details
 

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sambristol said:
Kenshi64 see attached for all the details

Did you type that out yourself? Cool, Thanks! I got most of it but the end was above me, and anyway its sufficient if you answer the doubt in words, since I'm not doing Physics in much detail.
 
I appreciate both the reply, but sadly I don't understand either, could you address the question directly without jumping into other complicated things! Thanks, I'm truly sorry for the inconvenience. :)
 
Tell me exactly what you don't understand and I will try my best to bridge the gap.

That is ask me specific questions

Physics is written in the language of maths. Separate the maths from the physics and much more importantly do not be afraid of either, the fear of the maths has hampered many a young physicist – not helped by professors who 'drop in' the maths so students don't know what is physics and what is maths

Regards

Sam
 

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