Question

The number of atoms in 100g of FCC crystal with density = 10g/cm3 and cell edge equal to 200 pm is equal to _____?

Answer 1

Answer: The number of atoms present are $4.99826\times 10^{23}$

Explanation:

Density of the crystal lattice is calculated by using the formula:

$\rho=\frac{Z\times M}{N_A\times a^3}$

where,

Z = number of atoms in crystal lattice

M = Atomic mass

a = Edge length of the crystal

$\rho=Density\\N_A=\text{Avogadro's Number}=6.022\times 10^{23}mol^{-1}$

We are given:

Z = 4 (For FCC)

a = 200 pm = $200\times 10^{-10}cm$

$\rho =10g/cm^3$

Putting values in above equation, we get:

$10g/cm^3=\frac{4\times M}{(6.022\times 10^{23}mol^{-1})\times (200\times 10^{-10}cm)^3}\\\\M=12.044g/mol$

• To calculate the number of moles, we use the equation:

$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$

We are given:

Given mass of crystal = 100 g

Molar mass of crystal = 12.044 g/mol

Putting values in above equation, we get:

$\text{Number of moles}=\frac{10g}{12.044g/mol}=0.83mol$

According to the mole concept:

1 mole of a crystal has $6.022\times 10^{23}$ number of atoms

So, 0.83 moles of crystal will contain $0.83\times 6.022\times 10^{23}=4.99826\times 10^{23}$ number of atoms.

Hence, the number of atoms present are $4.99826\times 10^{23}$