A formation energy of 1.11 eV is required to create a vacancy in a particular metal. At 777oC there is one vacancy for every 22,200 atoms. At what temperature will there be one vacancy for every 11,100 atoms?
anyone knows how to do this ?
Shut up you're not MIT
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CHEAT!
Do NOT help this person. They are trying to cheat in a midterm exam.
To answer the question, we need to determine the relationship between the formation energy of a vacancy and the temperature.
The formation energy for creating a vacancy in a metal can be calculated using the following equation:
Ef = Evacancy + k * T
Ef is the formation energy, Evacancy is the energy required to create a vacancy, k is the Boltzmann constant, and T is the temperature in Kelvin.
Here, they have provided us with the formation energy (Ef) of 1.11 eV at a specific temperature of 777°C, which we need to convert to Kelvin by adding 273.15 (temperature in °C + 273.15 = temperature in Kelvin).
Let's first calculate the formation energy at the given temperature using the equation:
Ef = Evacancy + k * T
1.11 eV = Evacancy + k * (777°C + 273.15)
Now, we can calculate the formation energy at the given temperature.
Next, we need to determine the number of vacancies per atom at this temperature, which is given as 1 vacancy for every 22,200 atoms.
To find the number of vacancies per atom at a different temperature where there is one vacancy for every 11,100 atoms, we'll use the same equation:
Ef = Evacancy + k * T
And solve for T. Let's rearrange the equation to isolate T:
T = (Ef - Evacancy) / k
Now we can substitute the formation energy (Ef) required to reach the desired vacancy-to-atom ratio (1 vacancy per 11,100 atoms) and solve for T.