31.3 Substructure of the nucleus  (Page 2/16)

where $A$ is also called the mass number    . This name for $A$ is logical; the mass of an atom is nearly equal to the mass of its nucleus, since electrons have so little mass. The mass of the nucleus turns out to be nearly equal to the sum of the masses of the protons and neutrons in it, which is proportional to $A$ . In this context, it is particularly convenient to express masses in units of u. Both protons and neutrons have masses close to 1 u, and so the mass of an atom is close to $A$ u. For example, in an oxygen nucleus with eight protons and eight neutrons, $A=\text{16}$ , and its mass is 16 u. As noticed, the unified atomic mass unit is defined so that a neutral carbon atom (actually a ${}^{\text{12}}\text{C}$ atom) has a mass of exactly 12 $\text{u}$ . Carbon was chosen as the standard, partly because of its importance in organic chemistry (see Appendix A ).

Let us look at a few examples of nuclides expressed in the ${}_Z^A{\text{X}}_N$ notation. The nucleus of the simplest atom, hydrogen, is a single proton, or ${}_1^1\text{H}$ (the zero for no neutrons is often omitted). To check this symbol, refer to the periodic table—you see that the atomic number $Z$ of hydrogen is 1. Since you are given that there are no neutrons, the mass number $A$ is also 1. Suppose you are told that the helium nucleus or $\alpha$ particle has two protons and two neutrons. You can then see that it is written ${}_2^4{\text{He}}_2$ . There is a scarce form of hydrogen found in nature called deuterium; its nucleus has one proton and one neutron and, hence, twice the mass of common hydrogen. The symbol for deuterium is, thus, ${}_1^2{\text{H}}_1$ (sometimes $\text{D}$ is used, as for deuterated water ${\text{D}}_2\text{O}$ ). An even rarer—and radioactive—form of hydrogen is called tritium, since it has a single proton and two neutrons, and it is written ${}_1^3{\text{H}}_2$ . These three varieties of hydrogen have nearly identical chemistries, but the nuclei differ greatly in mass, stability, and other characteristics. Nuclei (such as those of hydrogen) having the same $Z$ and different $N$ s are defined to be isotopes    of the same element.

There is some redundancy in the symbols $A$ , $\text{X}$ , $Z$ , and $N$ . If the element $\text{X}$ is known, then $Z$ can be found in a periodic table and is always the same for a given element. If both $A$ and $\text{X}$ are known, then $N$ can also be determined (first find $Z$ ; then, $N=A-Z$ ). Thus the simpler notation for nuclides is

which is sufficient and is most commonly used. For example, in this simpler notation, the three isotopes of hydrogen are ${}^1\text{H,}{}^2\text{H,}$ and ${}^3\text{H,}$ while the $\alpha$ particle is ${}^4\text{He}$ . We read this backward, saying helium-4 for ${}^4\text{He}$ , or uranium-238 for ${}^{\text{238}}\text{U}$ . So for ${}^{\text{238}}\text{U}$ , should we need to know, we can determine that $Z=\text{92}$ for uranium from the periodic table, and, thus, $N=\text{238}-\text{92}=\text{146}$ .

A variety of experiments indicate that a nucleus behaves something like a tightly packed ball of nucleons, as illustrated in [link] . These nucleons have large kinetic energies and, thus, move rapidly in very close contact. Nucleons can be separated by a large force, such as in a collision with another nucleus, but resist strongly being pushed closer together. The most compelling evidence that nucleons are closely packed in a nucleus is that the radius of a nucleus    , $r$ , is found to be given approximately by