Question

Compute the concentration (count per volume) of vacancies in copper at room temperature if the lattice parameter of FCC copper is 0.3615 nm at room temperature (25oC, 298 K), and the activation energy to form a single vacancy is 0.9 eV. Use 8.617x10-5 eV/(atom-K), exactly, as Boltzmann's Constant.

Note: You could look up the density and atomic weight of copper to compute room temperature atom concentration you need for this problem.

Answer 1

5.1044844 x 10^7/cm^3 = 5E7

Step-by-step explanation:

The atomic weight and density (at 25 ° C) for copper are 63.5 g/mol or 0.0635 kg/mol and 8,960 kg/m^3

First lets find the value of N, number of atomic sites per cubic meter for copper, from its atomic weight Acu, its density, and Avogadro’s number NA

N = NA x ρ / Acu = 6.023 x 10^23 x 8,960 kg/m^3 / 0.0635 kg/mol = 8.4985953 x 10^28 atoms / m3

Temperature dependency can be given as :

Arrhenius equation

Nv = N e^(-EA/KT)

N = no. of atoms initially

Ev = activation energy

Nv = 8.4985953 x 10^28 atoms / m^3 exp^-(0.9ev/atom /8.617x10-5 eV/(atom-K) x 298 K

Nv = 5.1044844 x 10^13 /m3

vacancies per cm^3 = 5.1044844 x 10^7/cm^3 = 5E7