Avogadro's Number Definition Numerical Value Additional

This physical constant is named after the early 19th century Italian scientist Amedeo Avogadro. It appears that Jean Baptiste Perrin was the first to name it. Perrin called it "Avogadro's constant" and it is still sometimes known by that name. The numerical value was first calculated by Johann Josef Loschmidt in 1865 using the kinetic gas theory. In the German language countries the number is still sometimes referred to as Loschmidt's number.

1 Definition

Avogadro's number is formally defined as the number of carbon-12 atoms in 0.012 kg of carbon-12. Historically, carbon-12 was chosen as the reference substance because its atomic weight could be measured particularly accurately.

Avogadro's number can be applied to any substance. It corresponds to the number of atoms or molecules needed to make up a mass equal to the substance's atomic or molecular weight, in grams. For example, the atomic weight of iron is 55.847 amu, so Avogadro's number of iron atoms (i.e. one mole of iron atoms) have a mass of 55.847 g. Conversely, 55.847 g of iron contains Avogadro's number of iron atoms. Thus Avogadro's number also corresponds to the conversion factor between grams (g) and atomic mass units:

2 Numerical value

At present it is not technologically feasible to count the exact number of atoms in 0.012 kg of carbon-12, so the precise value of Avogadro's number is unknown. The 1998 CODATA recommended value for Avogadro's number is

where the number in parenthesis represents the one standard deviation uncertainty in the last digits of the value.

A number of methods can be used to measure Avogadro's number. One modern method is to calculate Avogadro's number from the density of a crystal, the relative atomic mass, and the unit cell length determined from x-ray crystallography. Very accurate values of these quantities for silicon have been measured at the National Institute of Standards and Technology (NIST) and used to obtain the value of Avogadro's number.

3 Additional physical relations

Avogadro's number provides the link between a number of useful physical constants when we move between an atomic mass scale and a kilogram ( SIThe International System of Units (symbol: SI (for the French phrase Systeme International d'Unites , is the most widely used system of units. It is used for everyday commerce in virtually every country of the world except the United States, and it is uni) scale:

4 Connection to mass of protons and neutrons

A carbon-12 atom consists of 6 protonFor alternative meanings see proton (disambiguation). Proton Classification Subatomic particle Fermion Hadron Baryon Nucleon Proton Properties Mass: 938 MeV/ c2 Electric Charge: 1. 6 × 10−19 C Spin: 1/2 In physics, the proton is a subatomic particles and 6 neutronNeutron Classification Subatomic particle Fermion Hadron Baryon Nucleon Neutron Properties Mass: 940 MeV/ c 2 Electric Charge: 0 C Spin: 1/2 In physics, the neutron is a subatomic particle with no net electric charge and a mass of 940 MeV/ c 2 ( kg; verys (which have approximately the same mass) and 6 electronThe electron (also called negatron commonly represented as e&minus is a subatomic particle. In an atom the electrons surround the nucleus of protons and neutrons in an electron configuration. Electrons have the smallest electrical charge and when they movs (whose mass is negligible in comparison). One could therefore think that N_A is the number of protons or neutrons that have a mass of 1 gram. While this is approximately correct, the mass of a free proton is 1.00727 amu, so a mole of protons would actually have a mass of 1.00727 g. Similarly, a mole of neutrons has a mass of 1.00866 g. Clearly, 6 moles of protons combined with six moles of neutrons would have a mass greater than 12 g. So, you might ask how one mole of carbon-12 atoms, which should consist of 6 moles each of protons, neutrons, and electrons could possibly have a mass of only 12 g? What happened to the excess mass? The answer is related to the equivalence of matter and energy discovered by Albert Einstein as part of the theory of special relativity. When an atom is formed, the protons and neutrons in the nucleus are bound together by the strong nuclear force. This binding results in the formation of a low energy state and is accompanied by a large release of energy. Since energy is equivalent to mass, the released energy corresponds to a loss in the mass of the nucleus relative to that of the separated protons and neutrons. Thus, protons and neutrons in the nucleus have masses that are less (about 0.7 percent less) than free protons and neutrons. The precise amount of mass loss is related to the binding energy of the nucleus and varies depending on the type of atom.

One may therefore say that N_A is approximately the number of nuclear neutrons or protons that have a mass of 1 gram. This is approximate because the precise mass of a nuclear proton or neutron depends on the composition of the nucleus. For example, iron nucleons will have a significantly lower mass than those in hydrogen or plutonium.

5 Avogadro's number in life

Avogadro's number often yields practical reasonings in real life. For example, the fact that a finite number of atoms are in a given amount of a substance is one reason for scientific criticism of homeopathy, in which medicinal substances are often diluted to the extent that Avogadro's number would imply that less than a single molecule remains.

6 See also

7 Further Reading

Journal of Physical and Chemical Reference Data, 28 (1999) 1713.

8 External links

Some Notes on Avogadro's Number, 6.022 x 10²³ (historical notes)

Chemistry Dimensionless numbers

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