To solve this problem, it is necessary to take into account the concepts of the number of vacations N_v at a given temperature as well as the calculation of the number of atom sites per cubic meter.
For definition the number of atomic sites per cubic meter is given as,
Where,
Avogadro's number
density
A = Atomic weight
Replacing with our values we have
At the same time we know that the number of vacancies is defined as,
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Where,
Energy of vacancy
Boltzman constant
T = Temperature
Replacing with the values given we have
Therefore the number of vacancies per cubit meter at 1000°C is