Calculate the energy (in J/atom) for vacancy formation in silver, given that the equilibrium number of vacancies at 800 C is 3.6 x 1017/cm3. The atomic weight and density for silver are 107.9 g/mol and 9.5 g/cm3, respectively

the energy vacancies for formation in silver is

Explanation:

Given that:

the equilibrium  number of vacancies at 800 °C

i.e T = 800°C     is  3.6 x 10¹⁷ cm3

Atomic weight of sliver = 107.9 g/mol

Density of silver = 9.5 g/cm³

Let's first determine the number of atoms in silver

Let silver be represented by N

SO;

where ;

avogadro's number =

= Density of silver = 9.5 g/cm³

= Atomic weight of sliver = 107.9 g/mol

N = 5.30 × 10²⁸ atoms/m³

However;

The equation for equilibrium number of vacancies can be represented by the equation:

From above; Considering the  natural logarithm on both sides; we have:

Making the subject of the formula; we have:

where;

K = Boltzmann constant = 8.62 × 10⁻⁵ eV/atom .K

Temperature T = 800 °C = (800+ 273) K = 1073 K

Where;

1 eV = 1.602176565 × 10⁻¹⁹ J

Then

Thus, the energy vacancies for formation in silver is