# Describing and Comparing Atoms

Atoms can be described in terms of their size, atomic number, atomic weight, and ionic charge.

Atomic theory and the experiments that led to its development give a good picture of what makes up an atom, its size, and the sizes and masses of its components. At the time atomic theory began to be developed, it was not possible to study atoms directly, but in the time since, scientists have been able to view a single atom under a microscope. A microscope used for viewing an atom must have tremendous magnifying power, as atoms are only about 100 picometers ($1\times{10}^{-10}$ meters) in diameter.

The small size of atoms led scientists to coin a new measurement term to describe them: the angstrom (Å), a unit of length equal to 1010 meter. This unit is named for Swedish physicist Anders Jonas Ångström, whose work included the discovery that the sun contains hydrogen. One Å is equal to 100 pm, so one Å is about as long as one atom's diameter.
While atomic theory was emerging, scientists were discovering the subatomic particles that make up the atom. The periodic table, which lists all the elements along with their basic properties, was also being developed. The modern periodic table lists each element's atomic number, chemical symbol, and atomic weight. An atomic number (Z) is the number of protons in each atom of an element. An chemical symbol is the letter or letters used to represent an element—for example, C for carbon and He for helium. Atomic weight is the average mass of all the isotopes of an element, based on the relative abundance of each isotope.
Elements may also be described according to their mass number (A), the sum of the number of protons and neutrons in the nucleus. An atomic mass unit (amu) is the mass of a single proton or neutron, 1 gram per mole (g/mol), defined as one-twelfth the mass of a carbon-12 atom, approximately equal to $1.66 \times {10^{- 27}}{\;\rm{ kg}}$. A mol is equal to $6.022 \times {10^{23}}$, which is the number of atoms in 12 grams of carbon-12. The atomic number is the number of protons in an atom. The sum of the masses of all of the protons and neutrons in an atom measured in atomic mass units is the atomic mass of the atom. Atomic mass is the mass of a single atom, while atomic weight is an average measurement of many isotopes of an atom.

When describing atoms, it may also be useful to discuss their charge. The fundamental unit of charge (e) is the charge of an electron, $1.6021765 \times {10^{-19}}\;{\rm{ C}}$ (coulomb). A coulomb is a unit of electric charge. Atoms gain and lose electrons frequently, which changes the overall charge of the atom. When an atom has an equal number of protons and electrons, it is neutral, which means it has no net charge. If an atom or molecule gains or loses electrons, giving it a positive or negative charge, it is an ion. An atom or group of atoms that has more protons than electrons, giving it an overall positive charge, is a cation. An atom or group of atoms that has more electrons than protons, giving it an overall negative charge, is an anion. The ionic charge of an element can be written shorthand using a superscript, such as K+ for a potassium cation and O2– for an oxygen anion.

When writing the chemical symbol for an isotope, the mass number is sometimes written as a superscript before the letter: 14C, 35S, 3H. Alternatively, the name of the element can be written followed by a hyphen and the mass number: carbon-14, sulfur-35, hydrogen-3. Carbon-14 can also be written as ${}_6^{14}\rm{C}$, which indicates that the atomic number for carbon is 6 and the mass number for this particular isotope is 14. The number of neutrons the isotope has can be determined by subtracting the number of protons from the mass number.
$\text{mass number (A)}-\text{atomic number (Z)}=\text{number of neutrons}$
The isotope ${}_6^{14}\rm{C}$ has 8 neutrons: $14-6=8$.

Isotopes affect the atomic weight of an element, which is calculated as a weighted average of all isotopes based on their relative abundance. For example, oxygen has three isotopes with different relative abundances and atomic weights.

### Oxygen Isotopes

Isotope Relative Abundance (%) Atomic Weight (amu)
16O 99.757 15.995
17O 0.038 16.995
18O 0.205 17.999

Oxygen has three isotopes, each with a different relative abundance and atomic weight.

To calculate the atomic weight for oxygen, first multiply each isotope's relative abundance by its atomic weight:
$\begin{gathered}{}^{16}\rm{O}{:}\;0.99757\times15.995\;\rm{amu}=15.95613\;\rm{amu}\\{}^{17}\rm{O}{: }\;0.00038\times16.995\;\rm{amu}=0.006458\;\rm{amu}\\{}^{18}\rm{O}{: }\;0.00205\times17.999\;\rm{amu}=0.036898\;\rm{amu}\end{gathered}$
$15.95613\;\rm{amu}+0.006458\;\rm{amu}+0.036898\;\rm{amu}=15.999\;\rm{amu}$