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 interstital vacancies created by missing Ge atoms . In one such experiment , 1g 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 germination , which are filled up by boron atoms . (Aw of Ge = `72.6` and B = 11 ) (assume volume constant )

Options

A. `23%`
B. `2.3%`
C. `46%`
D. `80%`

Answer

B

Explanation

Assume here that the decrease in density is not due to volume change but due to loss of Ge atoms only. Let x be the tota numberof Ge atoms missing and y be the number of B atoms replacing Ge atoms. Assuming the volumne of crystal reamining saem, than 4% decrease in density will also decrease weight of the crstal (sample) by 4%.
`therefore 1-(x xx(72.6)/(N_(A)))+(y xx(11)/(N_(A)))=0.96`
`0.04=(x xx(72.6)/(N_(A)))-(y xx (11)/(N_(A)))`
`y=((150N_(A))/(10^(6)xx11)xx0.96)` or `(yxx11)/(N_(A))=((150xx0.96)/(10^(6)))`
`thereforex=((0.04+1.44xx10^(-4))N_(A))/(72.6)=(0.04N_(A))/(72.6)`
`therefore(y)/(x)=(150N_(A)xx0.96xx72.6)/(10^(6)xx11xx0.04N_(A))=2.376xx10^(-2)`
`therefore (y)/(x)xx100=2.376xx10^(-2)xx100=2.376%`