Question

Calculate the number of vacancies per cubic meter for some metal, M, at 783°C. The energy for vacancy formation is 0.95 eV/atom, while the density and atomic weight for this metal are 6.10 g/cm^3 (at 783°C) and 43.41 g/mol, respectively.

Answer 1

Answer:

Following are the solution to this question:

Explanation:

The number of vacancies by the cubic meter is determined.  

$N_V =N exp(\frac{Q_v}{kT})$

      $= \frac{N_A \rho}{A} exp (\frac{Q_v}{kT})$

      $= \frac{6.022 \times 10^{23} \times 6.10}{43.41} \exp(\frac{-0.95}{8.62\times 10^{-5} \times (783+273)})\\\\= \frac{36.7342 \times 10^{23}}{43.41} \exp(\frac{-0.95}{0.0313626})\\\\= 0.846215158 \times 10^{23} \exp(-30.290856)$

      $=1.57 \times 10^{25} \ cm^{-3}$