Calculate the approximate number of unit cells present in 1g of gold. Given that gold crystallizes in the face-centered cubic lattice. (Atom mass of gold = 197u)

Calculate the approximate number of unit cells present in 1g of gold. Given that gold crystallizes in the face-centered cubic lattice. (Atomic mass of gold = 197u)

Given Values

Type of unit cell = FCC

So, 1 U.C. is made up of = 4 atoms

Atomic Mass of gold = 197 gm/mol

Weight of gold = 1 gm

Calculations

Number of atoms in 1 gm of Gold

197 gm of gold  =  6.02 × 1023 atoms of gold

1 gm of gold =  $$\frac{6.02\times 10^{23}}{197}$$ atoms

Number of U.C. in 1 gm of gold

4 atoms of gold = 1 Unit Cell

$$\frac{6.02\times 10^{23}}{197}$$ atoms of gold =  $$\frac{6.02 \times 10^{23}}{197 \times 4}$$ U.C.

Therefore, there are  $$7.64\times 10^{20}$$ unit cells in 1 gm of gold.