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

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Homework Help Overview

The discussion revolves around isobars, specifically the isotopes 139/57 La, 139/59 Pr, and 139/55 Cs, focusing on their neutron to proton ratios and binding energies per nucleon. Participants are exploring how these factors relate to atomic masses and stability.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to calculate atomic masses and binding energies, with some questioning the existence of certain isotopes and the accuracy of their calculations. There is discussion on the importance of precision in these calculations.

Discussion Status

Some participants have provided references for more precise atomic masses, which may guide further calculations. There is an ongoing exploration of the relationships between neutron to proton ratios and binding energies, but no consensus has been reached on the correct approach or results.

Contextual Notes

Participants are working under the constraints of available atomic mass data and are questioning the validity of certain isotopes based on their references. The discussion highlights the need for precision in calculations related to binding energy.

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
1605996319506.png

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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