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

The answer to tnhe question is;

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

Step-by-step 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=(100)/(1+(N_A\rho_2)/(N_1A_1) -(\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)=(100)/(1+((6.022*10^(23))*(2.33))/((3.43*10^(21))*(72.64)) -((2.33)/(5.32)) ) = (100)/(1+5.632 -0.43797 ) = 16.146 %`

`C_(Ge)` = 16.146 %.