The vacancy fraction of a particular metal is found to double as the temperature of the metal is increased from 700 degrees C to 850 degrees C. Calculate the enthalpy of vacancy formation for this metal. Express your answer in units of eV.
To calculate the enthalpy of vacancy formation for the metal, we need to use the equation:
H = kT ln(V2/V1)
where H is the enthalpy of vacancy formation, k is the Boltzmann constant (8.617333262145 x 10^-5 eV/K), T is the temperature in Kelvin, and V1 and V2 are the vacancy fractions at temperatures T1 and T2, respectively.
First, we need to convert the temperatures from degrees Celsius to Kelvin:
T1 = 700 degrees C + 273.15 = 973.15 K
T2 = 850 degrees C + 273.15 = 1123.15 K
Next, we substitute the values into the equation:
H = (8.617333262145 x 10^-5 eV/K) * (1123.15 K - 973.15 K) * ln(2)
Calculating this expression gives us the enthalpy of vacancy formation for the metal in eV.