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

Following are the solution to this question:

Step-by-step explanation:

The number of vacancies by the cubic meter is determined.

`N_V =N exp((Q_v)/(kT))`

`= (N_A \rho)/(A) exp ((Q_v)/(kT))`

`= (6.022 * 10^(23) * 6.10)/(43.41) \exp((-0.95)/(8.62* 10^(-5) * (783+273)))\\\\= (36.7342 * 10^(23))/(43.41) \exp((-0.95)/(0.0313626))\\\\= 0.846215158 * 10^(23) \exp(-30.290856)\\\\`

`=1.57 * 10^(25) \ cm^(-3)`