In reply to [email protected]'s message of Wed, 14 Apr 2010 07:57:02 +1000: Hi, [snip] >I'm not so sure about this. The energy differences between the two atoms are >calculated based upon mass differences between *atoms*, which means that the >mass of the Mo atom is that of an atom with all it's electrons already in >place. >(actually this is not quite true; it's based on the mass of a singly or doubly >ionized atom with the mass of the appropriate number of electrons simply added >to it, however this electron(s) is/are the valence electrons and their binding >energy is just a few eV, so to all intents and purposes the masses are atomic >masses.) Note however that since they are already in place they have >effectively >already escaped from the nucleus, thus the energy stored in the potential >difference between electron and nucleus has already been accounted for. That in >turn means that the energy difference calculated based upon mass difference >should be available as kinetic energy over and above the energy required to >form >the new atom, IOW the electron(s) should be able to escape. >I realize that this diatribe isn't very clear, perhaps because it isn't very >clear in my mind either. However I hope you can follow my argument. [snip]
At 3 AM I realized that with the change in charge on the nucleus more potential energy is stored in all the remaining electrons, thus reducing the amount available as kinetic energy for the two decay electrons. In order to get a handle on how much energy this is, consider the following. The two innermost electrons of the Mo atom do a reasonable job of shielding (neutralizing) the charge of two protons in the nucleus, so to reasonable approximation, the rest of the Mo electrons "think" they are orbiting a Zr nucleus. If the two innermost electrons of the Mo atom are removed by x-ray absorption, then the remaining electrons suddenly "see" an Mo nucleus. This is essentially also what happens to the Zr electrons when double beta decay turns the Zr nucleus into an Mo nucleus, so the shift in potential energy of the remaining electrons in that case should be fairly similar to the x-ray absorption case for Mo. When the two innermost (K shell) electrons are removed from Mo, the process increases the potential energy of the remaining electrons of the then Mo ion. Consequently the increase in potential energy of the remaining electrons must be part of the energy received from the x-rays (first law). IOW the x-ray energy is greater than or equal to the potential energy stored in the remaining electrons, or put the other way around, the potential energy is less then the x-ray energy. The x-ray energy is fairly well known. For Mo it's 17445 + 19609 keV = 37354 eV. To make a long story short, the potential energy we can expect to be stored in the Zr electrons during double beta decay is about 40 keV (K shell electrons are not perfect shields). The actual decay energy is in the MeV range, so most of it will appear as kinetic energy of the decay electrons (and neutrinos). Regards, Robin van Spaandonk http://rvanspaa.freehostia.com/Project.html
