Nuclear Stability: A Comparison of Binding Energy and Packing Fraction

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SUMMARY

The discussion centers on the relationship between binding energy per nucleon and packing fraction in nuclear stability. The binding energy per nucleon is calculated using the formula mass defect multiplied by the speed of light squared divided by the mass number, while the packing fraction is derived from mass defect divided by mass number. A higher binding energy per nucleon indicates a more stable nucleus, whereas a smaller packing fraction suggests increased stability as well. The confusion arises from the differing definitions of mass defect in nuclear physics versus mass spectrometry.

PREREQUISITES
  • Understanding of nuclear physics concepts, specifically binding energy and mass defect
  • Familiarity with the formula for binding energy per nucleon
  • Knowledge of packing fraction and its implications in nuclear stability
  • Basic principles of mass spectrometry and its terminology
NEXT STEPS
  • Research the differences in mass defect definitions between nuclear physics and mass spectrometry
  • Study the implications of binding energy on nuclear stability in various isotopes
  • Explore the mathematical relationships between binding energy, packing fraction, and nuclear stability
  • Investigate advanced topics in nuclear physics, such as nuclear reactions and their energy considerations
USEFUL FOR

This discussion is beneficial for students and educators in nuclear physics, researchers exploring nuclear stability, and professionals in fields related to mass spectrometry and nuclear energy.

Krushnaraj Pandya
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Homework Statement


This is a conceptual question I have, the binding energy per nucleon is mass defect*c^2/mass number while the packing fraction is mass defect/mass number. A higher binding energy per nucleon indicates a more stable nucleus BUT a smaller packing fraction indicates a more stable nucleus as well despite BE/A=PF*c^2 as per the formulas- what blunder am I making?

Homework Equations


mentioned above

The Attempt at a Solution


mentioned above
 
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Let me re-frame the question, a higher mass defect means more energy to hold the nucleus together and a smaller atomic mass means less nucleons and radius, according to this a higher packing fraction should indicate a more stable nucleus not a less stable one, I'd be really grateful for any help to understand this-Thank you
 
can anyone solve this discrepancy?
 
Packing fraction is a term from mass spectrometry, in which "mass defect" is defined differently than in nuclear physics.
 

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