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 4.43 × 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

Let us take nO of atoms present in 1 cm^3 of pure Silicon.

= Density/mwt*Na

density = 2.33 g/cc

mwt = atomicmass of silicon = 28.09 g/mol

Na = avgadros number = 6.023*10^23 atoms/mol

= (2.33/28.09)*(6.023*10^23)

= 4.996*10^22 atoms/cc

mass of Ge-atoms present in 1 cc = ((4.43 × 10^21)/(6.023*10^23))*(72.64)

   = 0.5343 grams/cc

mass of Si-atoms present in 1 cc =

= (((4.996*10^22)-(4.43 × 10^21))/(6.023*10^23))*(28.09)

= 2.123 grams/cc

mass percentage of Ge = (0.5343/(0.5343+2.123))*100

= 20.11%