Answer:
1.10 eV/atom
Explanation:
The energy for vacancy formation can be calculated by solving the following equation for Qv:
[tex] N_{v} = N e^{-Q_{v}/kT} [/tex]
[tex] Q_{v} = -kT ln(\frac{N_{v}}{N}) [/tex] (1)
where Qv: is the energy required for vacancy formation, k: is the Boltzmann constant, T: is the temperature, N: is the concentration of atomic sites and Nv: is the vacancy concentration.
We have that:
Nv = 3.6x10²³ m⁻³
T = 1073 K
k = 8.62x10⁻⁵ eV/K
Hence, to calculate the energy for vacancy formation first we need to find N:
[tex] N = \frac{\rho N_{A}}{A} [/tex]
where ρ: is the density = 9.5 g/cm³, [tex]N_{A}[/tex]: is the Avogadro constant = 6.022x10²³ atoms/mol, and A: is the atomic weight = 107.9 g/mol.
[tex] N = \frac{9.5 g/cm^{3} 6.022 \cdot 10^{23} atoms/mol}{107.9 g/mol} = 5.30 \cdot 10^{28} m^{-3} [/tex]
Now, the energy for vacancy formation is:
[tex] Q_{v} = -8.62 \cdot 10^{-5} eV/atom*K \cdot 1073 K \cdot ln(\frac{3.6 \cdot 10^{23} m^{-3}}{5.30 \cdot 10^{28} m^{-3}}) = 1.10 eV/atom [/tex]
Therefore, the energy for vacancy formation in silver is 1.10 eV/atom.
I hope it helps you!
