You will recall from chemistry that atoms of different elements have different masses. The mass of an atom is determined primarily by its most massive constituents, the protons and neutrons in its nucleus. The sum of the number of protons and neutrons is called the atomic mass number $A$:

$A$, which by definition is an integer, is written as a leading superscript on the atomic symbol. For example, the common isotope of hydrogen, with one proton and no neutrons, is ${}^1\text{H}$. The “heavy hydrogen” isotope called deuterium, which includes one neutron, is ${}^2\text{H}$. The primary isotope of carbon, with six protons (which makes it carbon) and six neutrons, is ${}^{12}\text{C}$. The radioactive isotope ${}^{14}\text{C}$, used for carbon dating of archeological finds, contains six protons and eight neutrons.

The atomic mass scale is established by defining the mass of ${}^{12}\text{C}$ to be exactly 12 u, where u is the symbol for the atomic mass unit. That is, $m({}^{12}\text{C})=12\text{u}$. The atomic mass of any other atom is its mass relative to ${}^{12}\text{C}$. For example, careful experiments with hydrogen find that the mass ratio $m({}^1\text{H)/}m({}^{12}\text{C})$ is $1.0078\text{/}12$. Thus the atomic mass of hydrogen is $m({}^1\text{H})=1.0078\text{u}$.

The numerical value of the atomic mass of ${}^1\text{H}$ is close to, but not exactly, its atomic mass number $A=1$. For our purposes, it will be sufficient to overlook the slight difference and use the integer atomic mass numbers as the values of the atomic mass. That is, we’ll use $m({}^1\text{H})=1\text{u}$, $m({}^4\text{He})=4\text{u}$, and $m({}^{16}\text{O})=16\text{u}$. For molecules, the molecular mass is the sum of the atomic masses of the atoms forming the molecule. Thus the molecular mass of $\text{O}{}_2$, the constituent of oxygen gas, is $m(\text{O}{}_2)=32\text{u}$.

TABLE 18.2 shows the atomic mass numbers of some of the elements that we’ll use for examples and homework problems. A complete periodic table of the elements, including atomic masses, is found in Appendix B.

Very careful laboratory measurements have established that the mass of a ${}^{12}\text{C}$ atom in SI units is $m{(}^{12}\text{C})=1.993\times {10}^{-26}\text{kg.}$ Thus the conversion factor between atomic mass units and kilograms is

This conversion factor allows us to calculate the mass in kg of any atom or molecule. For example, a ${}^{20}\text{Ne}$ atom has atomic mass $m({}^{20}\text{Ne})=20\text{u}$. Multiplying by $1.66\times {10}^{-27}\text{kg}\text{/}\text{u}$ gives $m({}^{20}\text{Ne})=3.32\times {10}^{-26}\text{kg}$. If the atomic or molecular mass is specified in kilograms, the number of atoms or molecules in a system of mass $M$ is