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)

Answer:

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.

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