Explanation:
The number of vacancies per cubic meter are calculated as follows.
[tex]N_{v} = N exp (\frac{-Q_{v}}{kT})[/tex]
= [tex]\frac{N_{A} \rho}{A} exp(\frac{-Q_{v}}{kT})[/tex]
Putting the given values into the above formula as follows.
[tex]\frac{N_{A} \rho}{A} exp(\frac{-Q_{v}}{kT})[/tex]
= [tex]\frac{6.022 \times 10^{23} \times 5.49 g/cm^{3}}{50.02 g/mol} exp(\frac{-0.82}{8.62 \times 10^{-5} \times (723 + 273)})[/tex]
= [tex]0.661 \times exp(-9.55)[/tex]
= [tex]0.661 \times 7.120[/tex]
= 4.706 [tex]m^{3}[/tex]
Thus, we can conclude that number of vacancies per cubic meter for some metal, M, is 4.706 [tex]m^{3}[/tex].
