Final answer:
To calculate the fraction of atom sites that are vacant for copper at a given temperature, we need to use the energy for vacancy formation and the temperature. The fraction of atom sites that are vacant can be calculated using the equation: Vacancy Fraction = exp(-E_vacancy / (k * T)).
Step-by-step explanation:
To calculate the fraction of atom sites that are vacant for copper at a given temperature, we need to use the energy for vacancy formation and the temperature. The fraction of atom sites that are vacant can be calculated using the equation:
Vacancy Fraction = exp(-E_vacancy / (k * T))
Where E_vacancy is the energy for vacancy formation, k is the Boltzmann constant (8.617333262145 × 10-5 eV/K), and T is the temperature in Kelvin. Plugging in the values, we have:
Vacancy Fraction = exp(-0.90 / (8.617333262145 × 10-5 * 1232))
Vacancy Fraction = exp(-0.00008556)
Vacancy Fraction = 0.9999144
Therefore, the fraction of atom sites that are vacant for copper at a temperature of 959°C (1232 K) is approximately 0.9999144.