Question

Calculate the number of vacancies per cubic meter for some metal, M, at 749°C. The energy for vacancy formation is 0.86 eV/atom, while the density and atomic weight for this metal are 5.94 g/cm3 (at 749°C) and 80.09 g/mol, respectively.

Answer 1

Number of Vacancies = 1.22E23

Explanation:

Given

Energy for formation = 0.86 eV/atom (Q)

Density = 5.94 g/cm³

Atomic weight = 80.09 g/mol

Temperature = 749°C = 1022K

Avogadro's Constant = 6.022E23 atoms/mol

Boltzmann constant = 8.62E-5 eV/K (k)

Determination of the number of vacancies per cubic meter in metal, M at 749C (1022 K) is given by:

N exp (-Q/kT)

Where N = 6.022E23 * 5.94/ 80.09

N = 4.47E22

So, Number of Vacancies = 4.47E22 exp (-0.86 / (8.62E-5 * 1022))

= 4.47E22 exp (-9.76)

= 1.2150719773211E23

Number of Vacancies = 1.22E23 ------ Approximated