What nuclei are stable against beta decay?

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Discussion Overview

The discussion revolves around the stability of nuclei against beta decay, focusing on the criteria for determining whether specific nuclei, particularly even-odd and odd-even nuclei, are stable or unstable. Participants explore the role of binding energy, mass differences, and the use of the semi-empirical mass formula versus tabulated atomic masses.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • Some participants note that odd-odd nuclei are generally unstable against beta decay due to the pairing term in the semi-empirical mass formula being less than zero, while even-even nuclei are typically stable.
  • Others argue that beta decay can occur if the mass difference between two nuclei is greater than the mass of an electron and the charge difference is 1.
  • One participant emphasizes that the atomic mass found in tables includes the masses of atomic electrons, and a negative mass difference indicates that beta decay can occur.
  • There is a suggestion that the masses should be calculated using the semi-empirical mass formula, but others clarify that looking up measured values in tables is preferred.
  • A participant expresses concern about examination conditions and questions whether the semi-empirical mass formula would be used if tables are not available.
  • Another participant advises that the decision on using the semi-empirical mass formula depends on the instructor's goals for the course, noting that while it provides approximate results, tabulated masses are more accurate for decay energy calculations.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach for determining nuclear stability against beta decay, with differing views on the use of the semi-empirical mass formula versus tabulated values. The discussion remains unresolved regarding the specific criteria for even-odd and odd-even nuclei.

Contextual Notes

Limitations include the dependence on definitions of stability, the accuracy of the semi-empirical mass formula, and the availability of tables during examinations. There is also uncertainty regarding the pedagogical approach preferred by instructors.

Onias
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I know odd-odd nuclei are generally unstable against beta decay as the pairing term in the semi-empirical mass formula is less than zero, and I know even-even nuclei are generally stable, but I don't get the rules you apply for even-odd or odd-even nuclei. Do you have to work out the binding energy for beta +, beta - and electron capture daughter nuclei?
 
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It's not the binding energy. If the mass difference between two nuclei is greater than an electron mass, (and the charge difference is 1) beta decay can occur.
 
Meir Achuz said:
If the mass difference between two nuclei is greater than an electron mass, (and the charge difference is 1) beta decay can occur.

Note the added emphasis.

Beware that what you find in tables is generally the atomic mass which includes the masses of the atomic electrons. If the difference in atomic mass (final - initial) is negative, then beta decay can occur. See this post.
 
I assume that you calculate the masses using the semi-empirical mass formula, correct?
 
No, you look up the masses.
 
Onias said:
I assume that you calculate the masses using the semi-empirical mass formula, correct?

No, you look them up in a table of measured values. Atomic masses for most isotopes (except the very short-lived ones) have been measured to many significant figures. See here for example:

http://ie.lbl.gov/toimass.html
 
Last edited by a moderator:
That's great. I'm actually taking an examination soon. I hope the teacher is accommodating :) Hypothetically, though, if there weren't any tables in the exam, would I use the semi-empirical mass formula? Thanks again.
 
You had best ask your instructor about this. The answer depends on his goals for this course.

The semi-empirical mass formula gives only approximate results for the mass of any specific isotope. For calculating decay energies etc., I personally would use only tabulated masses, and provide my students with a table if they need it. However, your instructor may see some pedagogical value in using the semi-empirical formula for this, even though the results may not be very accurate.
 

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