What nuclei are stable against beta decay?

[Onias]

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?

 

[Meir Achuz]

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.

 

[jtbell]

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.

 

[Onias]

I assume that you calculate the masses using the semi-empirical mass formula, correct?

 

[Vanadium 50]

No, you look up the masses.

 

[jtbell]

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

 

[Onias]

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.

 

[jtbell]

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.