Mole: Avogadro's Number & Its Discovery

[akashpandey]

Why there is
1mole⇒6.022*10²³ atom.
Why there is not another number.
How avogrado find that number exactely correct at that time where there was no instuments.

 

[DrDu]

Avogadro did not find that number, it was only named after him. It's approximate value was first determined by Loschmidt in 1865:
http://books.google.de/books?id=ppEAAAAAYAAJ&pg=PA395#v=onepage&q&f=false
One mole was first defined as the number of atoms in 1g of hydrogen gas. As 1g is a fundamental unit in the cgs system, which is until today the preferred unit system in theoretical physics, this setting seems quite reasonable.

 

[akashpandey]

But why
1 mole ⇒6.022*10²³ atoms is their any derivation for it.

 

[DrDu]

It is the definition of the gram which is arbitrary and the number of atoms in one mole is purely empirical. The original definition of the gram was the mass of 1 cubic centimetre of water. At that time (end of the 18th century), one had no idea about the number of molecules that this amount might contain.