Number of constituent particles per moleThe Avogadro constant is the number of atoms, molecules, or other particles in one mole of a substance. Its value is approximately 6.022 × 10^23 per mole. This constant bridges the microscopic world of individual particles and the macroscopic world of grams and liters, allowing chemists and physicists to count particles by weighing bulk material.
The concept was introduced by Amedeo Avogadro in 1811, though he did not determine the number itself. The first accurate estimate came from Johann Josef Loschmidt in 1865, and the constant was later named in Avogadro's honor. The modern value was precisely determined in the 20th century through X-ray crystallography and other techniques.
The constant is defined so that the mass of one mole of a substance in grams equals its atomic or molecular mass in atomic mass units. For example, one mole of carbon-12 atoms has a mass of exactly 12 grams and contains Avogadro's number of atoms. This works because the atomic mass unit is defined as one-twelfth the mass of a carbon-12 atom, and the mole is defined as the amount of substance containing as many elementary entities as there are atoms in 12 grams of carbon-12.
The Avogadro constant is essential in chemistry for stoichiometry, in physics for defining the mole and the kilogram (until 2019, when the kilogram was redefined using the Planck constant), and in biology for calculating concentrations of solutions.
If you had Avogadro's number of pennies, they would cover the entire Earth's surface to a depth of about 1.6 kilometers.
| E | variable | Kinetic energy of the charged particle — energy joule |
| x | variable | Path length in the material — length metre |
| \rho | variable | Density of the absorbing material — density kilogram per cubic metre |
| z | variable | Charge number of the incident particle — charge number |
| A | variable | Atomic mass number of the absorber — atomic mass number |
| \beta | variable | Speed of the particle relative to the speed of light — velocity ratio |
| \gamma | variable | Lorentz factor of the particle — lorentz factor |
| v | variable | Speed of the particle — velocity metre per second |
| W_{\text{max}} | variable | Maximum energy transfer in a single collision — energy joule |
| I | variable | Mean excitation potential of the absorber — energy joule |
| \delta | variable | Density correction factor — density correction |
| C | variable | Shell correction factor — shell correction |
| Z | variable | Atomic number of the absorber — atomic number |
| N_A | constant | Number of constituent particles per mole — avogadro constant = 6.02214076e23 per mole |
| r_e | constant | Radius of a classical electron — classical electron radius = 2.8179403262e-15 metre |
| m_e | constant | Rest mass of the electron — electron mass = 9.1093837015e-31 kilogram |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| -\frac{d}{dx} | operator | Negative derivative with respect to path length — negative derivative |
| \ln | operator | Natural logarithm — natural logarithm |
