Nuclear Structure
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The Periodic Table
The periodic table is closely related to nuclear structure. The number of protons in the nucleus is responsible for the number of electrons surrounding the nucleus and therefore the chemical properties of the elements. Furthermore, the attractive force of the nucleus on the surrounding electrons along with quantum mechanics, determines the shapes of the electron orbitals. The structure of the nucleus can be more or less stable depending on both proton and neutron number. The half-life in the table above gives a sense of the stability. The half-life is the period that it takes for half of a sample to decay into something else. The gray entries are considered stable since they would only decay in a time greater than the age of the universe.
Chemical Symbols
When we write a symbol for an element like those seen on the periodic table above, we write , where X represents the element's name. In this notation, A is called the mass number which is also called the nucleon number, Z is the proton number, and N is the neutron number. A=Z+N relates the three numbers. Both the protons and neutrons are in the nucleus. All of the chemical properties of an element are dictated by Z, since that will also determine the electron structure that will surround the nucleus. The elements are named according to their value of Z, so it is redundant to include both the name and Z. Also, if Z is known, then we don't need both A and N. Most commonly we will include the name and A.
The reason the mass number can vary for different atoms of the same element is that different isotopes may exist, which are atoms with the same number of protons (which determines the name), but more or fewer neutrons. With that in mind, it is common to label isotopes of hydrogen, for instance as , or , etc. Both of these isotopes of hydrogen are rare on earth, but are plentiful in the sun. These two isotopes of hydrogen are common and vital to fusion processes in nature and are therefore given the proper names tritium and deuterium in addition to their chemical symbols.
Size of Nuclei
When thinking mostly of the size of a nucleus, the structure is often thought of as we would think of the hard packing of spheres. Given one ping pong ball, if we attach as second, third, etc, the cluster will have a radius that is essentially solved by simply realizing that each ball has a fixed volume, and A of them will have A times the volume. This is not entirely true due to the little gaps between spheres, but it is nearly correct. This relation can be written . More often we want the radius rather than the volume, and so by assuming a roughly spherical shape for both, we can write which naturally leads to where is shorthand for the radius of a single nucleon. In spite of the little gaps, this relationship holds quite well in comparison to experimental data.
While this volume relation stands up to experimental scrutiny, don't mistake the hard packing for a system of nucleons that are stuck in place as ping pong balls would be if they were glued together. In fact, nucleons seem to be very freely-moving within the confines of the nucleus. Clusters of 2 protons and 2 neutrons (which are called alpha particles) tend to move around freely within a nucleus and will occasionally break off of large, unstable nuclei.