The number of vacancies present in some metal at 757°C is 1.7 × 1024 m–3. Calculate the number of vacancies at 470°C given that the energy for vacancy formation is 1.17 eV/atom; assume that the density at both temperatures is the same.

1.14 * 10^18 cm^-3 or 1.14 * 10^24 m^-3

Explanation:

Using the formula

Nv = (6.022 * 10^23 atom/mol * density * e^(-1.17/8.62 * 10^-5 ev/atom.k * temperature))/weight

Since density= weight they both cancel out from the equation.

Nv == number of vacancy/ cubic meter

K == Temperature = 757°C = 273 + 757= 1030k

Nv = (6.022 * 10^23 atom/mol e^(-1.17/8.62 * 10^-5 ev/atom.k * 1030))

Nv = 6.022 * 10^23 * 1.892 * 10 ^-6

Nv = 1.4 * 10^18cm^-3 = 1.4 * 10^24m^-3

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