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What fraction of the surface of a crysta...

What fraction of the surface of a crystal of `Cd` at `T = 298 K` consists of vacancies? Assume that the energy needed to form a vacancy `= 0.5 Delta_("sub")H^(Θ)`. For `Cd(s), Delta_("sub")H^(Θ) = 112.0 kJ mol^(-1)`.

Text Solution

Verified by Experts

The number of vacancies (or Schottky defects) `(n)` is given by.
`n = Ne^(-E//2KT)` or `(n)/(N) = e^(-E//2KT)`
But fraction of the surface of a crystal vacancy is given by
`(n)/(N) = e^(E//2KT)`
`= exp[(-(0.5)(112.0xx10^(3)Jmol^(-1)))/((8.314JK^(-1)mol^(-1))(298 K))] = 1.5 xx 10^(-10)`
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