A strong current of trivalent gaseous boron passed through a germanium crystal decreases the density of the crystal due to part replacement of germanium by boron and due to interstitial vacancies created by missing Ge atoms. In one such experiment, one gram of germanium is taken and the boron atoms are found to be 150 ppm by weight, when the density of the Ge crystal decreases by 4%. calculate the percentage of missing vacancies due to germanium, which are filled up boron atoms. [Atomic wt. Ge=72.6, B=10] : 2.05% , 1.2%, 6.6%, none of above

Options

A. 0.098
B. 0.123
C. 0.047
D. 0.028

Answer

C

Explanation

Initially 1g Ge in `1cm^(3)`
Finally (1-x)g Ge and xg B in `1cm^(3)`
wt. of Ge decreases to 0.96g
Then, `(1-x)+(x xx11)/(72.6)=0.96` (72.6g Ge=11 g B)
On solving, x=0.047=4.7%