Answer to Question #2151 in Solid State Physics for JOEL LOBO

Question #2151
The fraction of vacancy sites in a metal is 1X10-10 at 500C. What will be the
fraction of vacancy sites at double the temperature?
1
Expert's answer
2011-03-24T06:13:20-0400

The fraction of vacant sites is given by the following expression:


"\\frac{N_{\\nu}}{N} = e^{\\left ( -\\frac{Q_{\\nu}}{kT} \\right )}"


At 500C we can find the activation energy :

"Q_{\\nu} = \\ln {\\frac{N_{\\nu}}{N}}kT = -\\ln{1 \\times 10^{-10}}\\cdot 8.31\\cdot(500+273) = 147909.5 \\ J\/mol"


At double temperature 1000C = 1000+273 = 1273K the fraction fo vacant sites is:

"\\frac{N_{\\nu}}{N} = e^{\\left ( -\\frac{147909.5}{8.31\\cdot1273} \\right )} = 0.85 \\times 10^{-8}"


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