callister7e_sm_ch04_24

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4-33 
 4.24 This problem asks us to determine the weight percent of Ge that must be added to Si such that the 
resultant alloy will contain 2.43 x1021 Ge atoms per cubic centimeter. To solve this problem, employment of 
Equation 4.19 is necessary, using the following values: 
 
 N1 = NGe = 2.43 x 10
21 atoms/cm3 
 ρ1 = ρGe = 5.32 g/cm3 
 ρ2 = ρSi = 2.33 g/cm3 
 A1 = AGe = 72.64 g/mol 
 A2 = ASi = 28.09 g/mol 
 
Thus 
 
 
CGe = 
100
1 + N AρSi
NGe AGe
 − ρSiρGe
 
 
 
 
= 100
1 + (6.023 × 10
23 atoms /mol)(2.33 g /cm3)
 (2.43 × 1021 atoms /cm3) (72.64 g /mol) − 
2.33 g /cm3
5.32 g /cm3
⎛ 
⎝ 
⎜ ⎜ 
⎞ 
⎠ 
⎟ ⎟ 
 
 
= 11.7 wt% 
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