Band of stability

Here’s the band of stability as it appears in my textbook:


[![Band of stability](https://i.stack.imgur.com/F1NHa.jpg)](https://i.stack.imgur.com/F1NHa.jpg)


1- My textbook states that the last stable atom is Pb-206 and every element that has an atomic number greater than 82 is radioactive. But if every dot resembles a stable atom, why aren’t the dots after Pb-206 in the graph considered stable?


2- Why is the $\frac{n}{p}$ ratio be $\frac{1.5}{1}$? Doesn’t that mean that for every proton there’s one and a *half* neutron?




The image is mislabeled: that red dot is 204 Hg, not 206 Pb.


Plus, the text is wrong: the "last" (heaviest) stable isotope is not lead-206, but lead-208!


The elements on the same vertical line of 206-Pb (which is 3 dots on the right of the mislabeled red dot) are 207-Pb and 208-Pb.
The last dot on the top right is 209-Bi. Bismuth was found in 2003 to be metastable (radioactive, with an extremely long half-life), so that chart might be older than that discovery.


A similar (and more accurate?) table, with colors and n and Z shown, can be found here:


<https://en.wikipedia.org/wiki/Table_of_nuclides_(combined)#Isotopes_for_elements_75-89>


The "1.5" ratio you mention comes from a linear fit. It means that not necessarily every single data fits it, but it represents well a general trend of the data. For instance, the image shows you that the ratio for 206-Pb "looks like" the 1.5 ratio, being 1.51.
Some other ratios are: 1.52 for 207-Pb, 1.55 for 204-Hg, etc...


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