Respuesta :
Answer:
a) The number of vacancies percubic centimeter is [tex]1.1573\times 10^{20} vacancy/cm^3[/tex].
b) The density of Lithium is [tex]1.076 g/cm^3[/tex].
Explanation:
Edge length of the lithium unit cell = a = [tex]3.5089\times 10^{-8} cm[/tex]
Volume of the unit cell = V
[tex]V=a^3=(3.5089\times 10^{-8} cm)^3=4.3203\times 10^{-23} cm^3[/tex]
The lithium crystal has one vacancy per 200unit cells.
[tex]\frac{1}{200} vacancy/unit cell=0.005[/tex] vacancy/unit cell
The number of vacancies percubic centimeter:
[tex]\frac{0.005}{V}=\frac{0.005 vacancy}{4.3203\times 10^{-23} cm^3}[/tex]
[tex]=1.1573\times 10^{20} vacancy/cm^3[/tex]
The number of vacancies percubic centimeter is [tex]1.1573\times 10^{20} vacancy/cm^3[/tex].
b)
Atomic mass of lithium = 7 g/mol
Number of atom in a unit cell = z = 2
Volume of the unit cell = V
[tex]\rho =\frac{z\times M}{N_A\times V}[/tex]
[tex]=\frac{4\times 7g/mol}{6.022\times 10^{23} mol^{-1}\times 4.3203\times 10^{-23} cm^3}=1.076 g/cm^3[/tex]
The density of Lithium is [tex]1.076 g/cm^3[/tex].
