What is the Isobar Binding Energy and How Does it Affect Atom Masses?

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SUMMARY

The discussion centers on isobars, specifically the isotopes 139/57 La, 139/59 Pr, and 139/55 Cs, and their binding energies and neutron-to-proton ratios. The stable isotope 139/57 La exhibits the highest binding energy, while the radioactive isobar 139/59 Pr is noted to be non-existent according to some sources. The importance of precision in atomic mass calculations is emphasized, as small discrepancies can significantly affect binding energy results. A reference for more precise atomic masses is provided, highlighting the need for accuracy in these calculations.

PREREQUISITES
  • Understanding of nuclear physics concepts, particularly isobars and isotopes.
  • Familiarity with binding energy calculations and the significance of neutron-to-proton ratios.
  • Knowledge of atomic mass units and how to accurately determine atomic masses.
  • Access to reliable nuclear data sources for atomic mass values.
NEXT STEPS
  • Research the binding energy calculations for different isotopes using precise atomic mass data.
  • Learn about the stability of isotopes and the factors affecting their decay processes.
  • Explore the concept of neutron-to-proton ratios in nuclear stability and decay.
  • Investigate the latest nuclear databases for accurate atomic mass values and their applications.
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Students and professionals in nuclear physics, researchers studying isotopic stability, and anyone involved in nuclear chemistry or atomic mass calculations.

jjson775
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Homework Statement
Nuclei having the same mass numbers are called isobars. The isotope 139/57 La is stable. A radioactive isobar 139/59 Pr decays by e+ emission. Another radioactive isobar 139/55 Cs, decays by e- emission. a) Which of these 3 isobars has the highest neutron to proton ratio? b) Which has the greatest binding energy per nucleon?
Relevant Equations
See below
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36FAA667-5ACC-47C7-B317-0159655CF1F2.jpeg
 
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jjson775 said:
Homework Statement:: Nuclei having the same mass numbers are called isobars. The isotope 139/57 La is stable. A radioactive isobar 139/59 Pr decays by e+ emission. Another radioactive isobar 139/55 Cs, decays by e- emission. a) Which of these 3 isobars has the highest neutron to proton ratio? b) Which has the greatest binding energy per nucleon?
Relevant Equations:: See below

View attachment 272898
View attachment 272899
How are you calculating the atomic masses of the isotopes? I just looked them up, and calculate that the La has the highest binding energy, as expected for the most stable.
 
139/59 Pr does not exist according to my table. So, to calculate the atomic mass to use in the binding formula, I used 140.908 for 141 Pr and subtracted the mass of 2 neutrons to give me an atomic mass of 138.9 for 139 Pr., as shown in the picture of my work. Apparently, my reasoning is wrong because the binding energy I get is too big.
 
jjson775 said:
139/59 Pr does not exist according to my table. So, to calculate the atomic mass to use in the binding formula, I used 140.908 for 141 Pr and subtracted the mass of 2 neutrons to give me an atomic mass of 138.9 for 139 Pr., as shown in the picture of my work. Apparently, my reasoning is wrong because the binding energy I get is too big.
At https://onlinelibrary.wiley.com/doi/pdf/10.1002/9783527618798.app2 it is given as 138.9089322.
The problem with your approximation method is that all three will have binding energies (correction: I mean, of course, atomic masses) close to 138.9, so precision is crucial.
 
Last edited:
Thanks. I found a reference with more precise atom masses.
 

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