Avogadro’s Number is 6.0221415 X 1023 which is also quantified as N A. “Avogadro’s number, N A , is the fundamental physical constant that links the macroscopic physical world of objects that we can see and feel with the submicroscopic, invisible world of atoms. In theory, N A specifies the exact number of atoms in a palm-sized specimen of a physical element such as carbon or silicon.” From Ronald Fox, Theodore Hill in American Scientist
An explanation of how Avogadro’s number helps comprehension at the atomic scale is explained on ThinkQuest – Projects by Students for Students:
avogadro’s number & the mole
“Avogadro’s number and the mole are very important to the understanding of atomic structure. The Mole is like a dozen. You can have a dozen guitars, a dozen roosters, or a dozen rocks. If you have 12 of anything then you would have what we call a dozen. The concept of the mole is just like the concept of a dozen. You can have a mole of anything. The number associated with a mole is Avogadro’s number. Avogadro’s number is 602,000,000,000,000,000,000,000 (6.02 x 1023). A mole of marbles would spread over the surface of the earth, and produce a layer about 50 miles thick. A mole of sand, spread over the United States, would produce a layer 3 inches deep. A mole of dollars could not be spent at the rate of a billion dollars a day over a trillion years. This shows you just how big a mole is. This number is so large that it is usually only represented in scientific notation:
6.02 x 1023
“Probably the only thing you will ever have a mole of is atoms or molecules. One mole of magnesium atoms (6.02 x 1023 magnesium atoms) weigh 24.3 grams. 6.02 x 1023 carbon atoms weigh a total of 12.0 grams. 6.02 x 1023 molecules of CO2 gas only weigh a total of 44.0 grams.
The decimal number on the periodic table is the atomic mass, the mass of one atom measured in atomic mass units (amu). Amu’s are defined to be 1/12 the weight of the most common isotope of Carbon. This number in grams is the mass of 1 mole of that element. For example, 6.02 x 1023 iron atoms weigh only 55.847 grams.(This is equivalent to saying one mole of iron atoms weigh 55.847 grams.) One mole of sulfur weighs 32.066 grams. (This is the same as saying 6.02 x 1023 Sulfur atoms weigh 32.066 grams) As mentioned earlier, one proton weighs 1.0073 amu and 1 neutron weighs 1.0087 amu. So the atomic mass is the mass in amus of one atom of an element, but you rarely use the mass of one atom. Even if you have a tiny speck of a metal or a microgram of an element, you have billions and billions of atoms. Thus, the mass in grams of one mole of an element (the gram atomic weight) is more useful.”