Physicopoeia

φυσικοποιΐα
THINGS I WISH I'D KNOWN WHEN I STARTED TEACHING PHYSICS

The Binding Energy Curve - which way round should it be?

Firstly, I'm assuming that 'the Binding Energy curve' makes you think of something like this:

 

Here's a worksheet which, over several pages, introduces the idea of Binding Energy and guides the reader to plotting a simplified Binding Energy curve stage by stage.

 

In these files, you will probably notice that I insist that Binding Energies are negative which might mean the graphs look upside down to you. Certainly I'm not in a majority in this: here's a Google image search which shows only about one in every 15 graphs plotted (what I would call) the right way round. This might be more convenient, but it's not correct Physics.

Not only must binding energy be negative because work must be done ON (not by) the nucleons to separate them but, once you have the graph plotted as a 'dip' rather than a 'hill', you can hopefully see how fission and fusion result in nuclei going 'downhill' in energy terms and hence it's clearer why these processes result in a release of energy.

Until more textbooks and exam boards come around to this point of view, I'm left having to warn my pupils that they will usually see the curve plotted the other way round, but simply to 'deal with it', as it were. Most seem happy to do so, in the slightly smug knowledge that their understanding is superior.

As a nice extension to this, you can turn the binding energy curve into a 3D plot with N, Z and binding energy on the three axes which then becomes something called the Nuclear Valley. This can explain not only fission and fusion, but also radioactive decay as well. This is where having the binding energies as negative numbers really starts to make sense as you can see how radioactive decay, fission and fusion all involve a decrease in Binding Energy. Here's a video which explains it all very nicely, although the narrator's idiosyncratic pronunciation might cause some smiles in places. The University of York's nuclear physics group has also produced some videos which cover similar ground, but they have gone one better by building a Lego nuclear valley!

WHICH IS THE MOST STABLE (TIGHTLY BOUND) NUCLEUS?

Countless textbooks and other sources state that Iron-56 is the most tightly-bound nucleus, i.e. that it has the minimum (or maximum, if you disagree with my insistence on minus signs, above) binding energy per nucleon. From my Excel file above, this looks correct. But, for simplicity, my file only includes the most abundant isotope of each element. If you include every isotope known, it turns out that Iron-58 and Nickel-62 are, in fact, slightly more tightly bound than Iron-56, though the differences aren't large (less than 0.05%).

It's not obvious where this misunderstanding came from. In fact, a whole paper was published some years ago, trying (inconclusively) to account for it, which Hyperphysics summarises admirably well. The original paper is:

Fewell M (1995). The atomic nuclide with the highest mean binding energy. American Journal of Physics (63:653)