Question

Germanium forms a substitutional solid solution with silicon. Compute the number of germanium atoms per cubic centimeter for a germanium-silicon alloy that contains 15 wt% Ge and 85 wt% Si. The densities of pure germanium and silicon are 5.32 and 2.33 g/cm3 , respectively.

Answer 1

Answer:

The number of germanium atoms per cubic centimeter for this germanium-silicon alloy is 3.16 x 10²¹ atoms/cm³.

Explanation:

Concentration of Ge ($C_{Ge}$) = 15%

Concentration of Si (C$_{Si}$) = 85%

Density of Germanium (ρ$_{Ge}$) = 5.32 g/cm³

Density of Silicon (ρ$_{Si}$) = 2.33 g/cm³

Atomic mass of Ge (A$_{Ge}$)= 72.64 g/mol

To calculate the number of Ge atoms per cubic centimeter for the alloy, we will use the formula:

No of Ge atoms/cm³=[Avogadro's Number*$C_{Ge}$]/([$C_{Ge}$*A$_{Ge}$/ρ$_{Ge}$)+(C$_{Si}$*A$_{Ge}$/ρ$_{Si}$)]

                              = (6.02x10²³ * 15%) / [(15% * 72.64/5.32)+(72.64*85%/2.33)]

                              = (9.03x10²²)/(2.048+26.499)

                              = (9.03x10²²)/(28.547)

No of Ge atoms/cm³ = 3.16 x 10²¹ atoms/cm³