MadSci Network: Physics

Re: Nucleons and the Atom

Date: Sun Jan 15 11:31:06 2006
Posted By: Michael Kay, President and Consultant AMBRY, Inc., and
Area of science: Physics
ID: 1136562139.Ph

You can rest assured that there is no error in your textbook. There are 
no stable nuclei with atomic mass number 5, and there are no radioactive 
(unstable) nuclei with atomic mass number 5 that have a half life greater 
than 10E-21 second. 

The reason for this lies in Binding Energy calculations. If this topic is 
not in your textbook, a good reference is William D. Ehmann and Diane E. 
Vance, "Radiochemistry and Nuclear Methods of Analysis", Wiley-
Interscience, New York, 1991, pages 70 to 74. You can reach many web 
pages on this topic by using a search engine, such as Google(c), 
on "Binding Energy". The entire first page is good sites with the 
exception of the gravitational binding energy of two stars. 

Information on the nuclear masses needed to calculate the binding energy 
can be found in the Table of Isotopes starting on Page 585 in Ehmann & 
Vance, or on the "Chart of the Nuclides" 15th Edition, Revised 1996 
Courtesy of Knolls Atomic Power Laboratory, Schenectady, NY, which is 
operated for the U.S. Department of Energy by KAPL, Inc., a Lockheed 
Martin Company Distributed by General Electric Nuclear Energy. This 
reference began in 1968 and has been carried forward to today. It has a 
long introduction that includes Nuclide Stability. The Lawrence Berkeley 
version of the Table of Isotopes is available on line as the first site 
listed when searching "Table of Isotopes" on Google.

All of these references indicate that He-5 and Li-5 are totally unstable, 
decaying in less than 10E-21 second. The extreme stability of He-4 as the 
product nucleus of decay gives:
He-5 going to He-4 plus a neutron
Li-5 going to He-4 plus a proton. 

To do the binding energy calculation for a specific nuclide, you take the 
mass of (total mass of protons) + (total mass of neutrons) and subtract 
the measured atomic mass of that nucleus. If Z is the proton number, and 
N is the neutron number, BE = {Z (mass of proton) + N (mass of neutron)}- 
atomic mass. Often the results are given in MEV (Million Electron Volts) 
by converting mass to energy using the Einstein Equation E = Mc^2.

For He-5 this is BE = {2(1.007825)+3(1.008665)} - 5.0122 = 0.02944 AMU
(this is 931.5 MEV/AMU x 0.02942 AMU or 27.4 MEV binding energy)

For He-4 this is BE = {2(1.007825)+2(1.008655)} - 4.00260 = 0.03036 AMU
(this is 931.5 MEV/AMU x 0.03036 AMU or 28.28 MEV binding energy)

This calculation shows that the binding energy for He-4 is 0.9 MEV 
greater than the binding energy for He-5 (it would take more energy to 
break apart an He-4 nucleus than an He-5 nucleus), and that the He-4 
nucleus is more stable. The He-5 nucleus gains 0.9 MEV of stability by 
emitting a neutron and becoming an He-4 nucleus. This difference is the 
reason for the insability of He-5 (and also Li-5 when you do the 

The calculation for Li-5 decaying by proton emission to He-4 is done the 
same way, and I leave that as an exercise for you.


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