As you can see here, there are a couple hundred

stable nuclides. Meaning that these stable nuclides and these

alone have the correct ratio of neutrons to protons. Too high of a ratio of neutrons to protons

and a neutron is turned into a proton and an electron, again, beta decay. Too high of a ratio of protons to neutrons

and a proton is turned into a neutron and an anti electron positron decay. Lots of scientists have thought a long time

about how this correct ratio could be specified in a formula, and what factors influence this

ratio. As implied by the line here on our z versus

n graph, it would be great if we could describe a line that went through the stable nuclides. Scientists have actually done a good job of

this and they have found among other things, having an odd or even number of nucleons affects

stability. Here is a graph of a particular group of nuclides

with an even number of nucleons, namely 102 neutrons and protons together. The horizontal axis gives the number of protons

or z of the particular nuclide. And the vertical axis gives the energy of

the ground state. Looking at this graph we can see why some

nuclides are unstable. They are trying to get to the bottom of this

energy valley by changing neutrons into protons or protons into neutrons driven by the energy

difference between their ground state and the ground states of the nuclei at the bottom

of the valley. Think of water falling on upper slopes of

a mountain valley. Driven by gravity, the water loses its potential

energy by running down the slope to the river at the bottom of the valley. The graph is typical for even number nuclides

for a given A. There are usually two stable nuclides at the bottom of the valley, in this

case rubidium 102 and palladium 102. You can also see that there are actually two

valleys here. One is for even even nuclides, which have

lower ground state energy, and odd odd nuclides, which have higher energy and are, therefore,

more likely to decay. For odd number of nucleons, the graph looks

quite different. In order to be odd, there must either be an

odd number of either protons or neutrons with an even number of the other sort of nucleon. The energy valley is generally steeper than

even A valleys, meaning there is more driving force in decay, and there is usually a single

stable nuclide at the bottom of the valley. In this particular case, it is barium 135. If we look at all the stable nuclides as a

whole, 60% of the stable nuclides are even-even, 38 percent are either even-odd or odd-even,

and a mere 2 percent of stable nuclides having an odd number of neutrons and an odd number

of neutrons and an odd number of protons are stable, and these are at such low z that the

nuclides have no choice. If you will, they are forced to be odd-odd

and there is just not room to maneuver. Looking again at our graph of stable nuclides

plotted as a function of z versus n, we also note there are what are called magic numbers. These magic numbers are favored by the nucleus

just as closed atomic shells make atoms unreactive chemically because they are already at their

lowest energy. Thus noble gasses are produced by closed shells. Likewise, it seems there is some short of

shell within the nucleus that produces a lower energy ground state making the nuclides exceptionally

stable. These magic numbers are 2, 8, 20, 28, 50,

and 82. Nuclides that have double magic numbers of

neutrons and protons are exceptionally stable. Helium 4, having two neutrons and two protons,

is in a class all by itself. It is so stable that it can be ejected from

a large nucleus as a form of decay. We call this alpha decay.

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