Question

Germanium forms a substitutional solid solution with silicon. Compute the weight percent of germanium that must be added to silicon to yield an alloy that contains 3.43 × 1021 Ge atoms per cubic centimeter. The densities of pure Ge and Si are 5.32 and 2.33 g/cm3, respectively. The atomic weights for germanium and silicon are 72.64 and 28.09 g/mol, respectively.

Answer 1

Answer:

The answer to tnhe question is;

The weight percent of germanium to be added is 16.146 %.

Explanation:

To solve the question, we note that  the formula to calculate the weight percent of an element in terms of the number of atoms per cm³ in a 2 element alloy is given by,

$C_1=\frac{100}{1+\frac{N_A\rho_2}{N_1A_1} -\frac{\rho_2}{\rho1} }$

Where

N$_A$ = Avogadro's Number

ρ₁ = Density of alloy whose weight percent is sought

ρ₂ = density of the other alloy

N₁ = Number of atoms per cubic centimeter

A₁ = Atomic weight of the element whose weight percent is sought

Therefore

$C_{Ge}=\frac{100}{1+\frac{(6.022*10^{23})*(2.33)}{(3.43*10^{21})*(72.64)} -(\frac{2.33}{5.32}) } = \frac{100}{1+5.632 -0.43797 } = 16.146 %$

$C_{Ge}$ = 16.146 %.