Question

Calculate the energy (in eV/atom) for vacancy formation in some metal, M, given that the equilibrium number of vacancies at 570°C is 2.13×10 m The density and atomic weight (at 570°C) for this metal are 15.1g/cm and 174.4g/mol, respectively

a) 0.88 eV/atom
b) 1.12 eV/atom
c) 1.32 eV/atom
d) 1.45 eV/atom

Answer 1

The energy for vacancy formation in the metal is approximately 1.32 eV/atom.

Step-by-step explanation:

To calculate the energy for vacancy formation in the metal, we can use the equation:

ΔE = kT x ln(N/n)

Where ΔE is the energy, k is the Boltzmann constant (8.617333262145x10⁻⁵ eV/K), T is the temperature in Kelvin (570 + 273 = 843 K), N is the total number of atomic sites (which is the same as the number of atoms per unit volume), and n is the equilibrium number of vacancies.

Plugging in the given values, we get:

ΔE = (8.617333262145x10⁻⁵ eV/K) x (843 K) x ln(15.1 g/cm³ / (2.13x10²² vacancies/cm³))

ΔE ≈ 1.32 eV/atom