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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)`.

A

`1.5 xx 10^(-10)`

B

`3 xx 10^(-5)`

C

`2 xx 10^(-6)`

D

`3 xx 10^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
A
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//RT)`
`="exp"[(-(0.5)(112.0xx10^(3)J"mol"^(-1)))/(8.314JK^(-1)"mol"^(-1)(298K))]=1.5xx10^(-10)`
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