Question

Calculate the number of vacancies per cubic meter for some metal, M, at 723°C. The energy for vacancy formation is 0.89 eV/atom, while the density and atomic weight for this metal are 5.49 g/cm3 (at 723°C) and 50.02 g/mol, respectively.

Answer 1

Explanation:

The number of vacancies per cubic meter are calculated as follows.

             $N_{v} = N exp (\frac{-Q_{v}}{kT})$

                      = $\frac{N_{A} \rho}{A} exp(\frac{-Q_{v}}{kT})$

Putting the given values into the above formula as follows.

            $\frac{N_{A} \rho}{A} exp(\frac{-Q_{v}}{kT})$

               = $\frac{6.022 \times 10^{23} \times 5.49 g/cm^{3}}{50.02 g/mol} exp(\frac{-0.82}{8.62 \times 10^{-5} \times (723 + 273)})$

               = $0.661 \times exp(-9.55)$

               = $0.661 \times 7.120$

               = 4.706 $m^{3}$

Thus, we can conclude that number of vacancies per cubic meter for some metal, M, is 4.706 $m^{3}$.