Avogadro's constant
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The SI definition of Avogadro's constant (designated NA) is: the number of entities (such as atoms, ions, or molecules) per mole. (This definition requires a definition of mole that does not rely on NA, but one that is in terms of 12C atoms). In the present definition NA has dimension mol−1. The numeric value of Avogadro's constant is NA = 6.022 141 79 x 1023 mol−1.
Because the mole and Avogadro's number are defined in terms of the atomic mass constant (one twelfth of the mass of a 12C atom), Avogadro's constant and number have by definition the same numerical value. In practice the two terms are used interchangeably.
See for more details, about the history of the determination of the constant, etc. Avogadro's number.