Question

Q. 13. In a metallic gold crystal, there is cubic centred
lattice. What is the approximate number of unit
cells present in 2.0 gm of gold? Atomic weight of
gold is 179.​

Answer 1

In a metallic gold crystal, there is cubic centred

lattice. What is the approximate number of unit

cells present in 2.0 gm of gold? Atomic weight of

gold is 179.

Answer 2

1.68 x 10²¹ unit cells are present in 2.0 gm of Gold.

Step-by-step explanation:

Given:

The given mass of gold = 2.0 gm.

Molar mass of gold = 179 g/mol

To find:

The number of unit cells of Au in 2.0 gm of gold.

Formula to be used:

Number of moles = given mass / molar mass.

Z (packing factor) = number of atoms present per unit cell

Step 1 of 2

The moles of gold crystal = given mass /  molar mass

$n=\frac{2}{179} \\\\n=0.0112$

In 1 mole of gold 6.022 x 10²³ atoms are present.

The number of atoms in 0.0112 moles of Au are =  0.0112 x 6.022 x 10²³

= 0.067 x 10²³ atoms

Step 2 of 2

In each unit of FCC unit cell, there are a total of 4 atoms present.

4 atoms = 1 unit cell

0.067 x 10²³ atoms will have unit cells =

$\frac{1*0.067*10^{23}}{4} \\\\=0.0168*10^{23}\\\\=1.68*10^{21}$

1.68 x 10²¹ unit cells are there in 2 gm of Au.