Early atomic theory began with Ancient Greek philosophers, who believed all matter was made of four elements, but Democritus proposed the existence of indivisible particles called atoms.

Key scientific laws established:

• Law of Conservation of Mass (Lavoisier, 1785): Mass is neither created nor destroyed in chemical reactions.

• Law of Definite Proportions (Proust, 1794): Compounds have constant composition by mass.

John Dalton's atomic theory (1808) stated:

• All matter is made of solid, indivisible atoms.

• Atoms are indestructible and retain identity in chemical reactions.

• Atoms of the same element are identical; atoms of different elements differ in mass and properties.

• Compounds are formed from elements in small whole-number ratios.

Atoms are composed of three subatomic particles:

• Protons (positive charge, in nucleus)

• Neutrons (neutral, in nucleus)

• Electrons (negative charge, outside nucleus)

Most of an atom's volume is empty space; the nucleus is extremely small but contains most of the atom's mass.

The overall charge of an atom is determined by the difference between the number of protons and electrons: Charge=Number of protons−Number of electrons

Each atom is defined by its atomic number (Z, number of protons) and mass number (A, total number of protons and neutrons):

• A=Number of protons+Number of neutrons

Changing the number of protons changes the element; atoms of the same element with different numbers of neutrons are called isotopes.

Isotopes are useful in tracing and dating samples in various sciences (e.g., biology, geology, archaeology). For example, 14C in tooth enamel can be used to estimate year of birth.

Isotopes of an element differ in mass; this difference allows their identification and quantification using mass spectrometry, which produces a spectrum showing the proportion of each isotope in a sample.

Most elements exist as mixtures of isotopes. The atomic mass on the periodic table is a weighted average of all naturally occurring isotopes, calculated as: Atomic mass=∑i(fractional abundance of isotope i×mass of isotope i)

Example: Silicon has three naturally occurring isotopes with different abundances and masses; the average atomic mass is calculated using their relative abundances and masses.