Answer:
1) 1.808 *10^8 vacancies per cm^3
2) 101,64ºC
Explanation:
You can use the following equation relating the number of vacancies with the energy required to produce them and the temperature:
[tex]n_{v} =Ne^{\frac{-E}{K_{b}*T} }[/tex]
Where N is the number atoms per unit of volume, you can calculate this number with the density of copper:
[tex]8.96 \frac{g}{cm^{3} } *\frac{1 mole copper}{63.54 g } *\frac{6.023*10^{23} atoms }{1 mole} = 8.47*10^{22}atoms[/tex]
And you can substitute all values in the equation:
[tex]n_{v} =8.47*10^{22}atoms*e^{\frac{-20 000 cal}{6.023*10^{23}mol^{-1}*3.297*10^{-24}cal*k^{-1}*298.15K} }=1.808*10^{8}atoms[/tex]
Now you solve for temperature and and use n as 1000 times the value of before:
[tex]T=\frac{-E}{k_{b}ln(n/N)} =\frac{-(2*10^{4}cal)}{(3.297*10^{24}calk^{-1})*ln(1.8083*10^{11}/8.47*10^{22})} =374.79 K = 101.64 C[/tex]
