## Related questions with answers

Silicon used in computer chips must have an impurity level below $10^{-9}$ (that is, fewer than one impurity atom for every $10^9 \mathrm{Si}$ atoms). Silicon is prepared by the reduction of quartz $\left(\mathrm{SiO}_2\right)$ with coke (a form of carbon made by the destructive distillation of coal) at about $2000^{\circ} \mathrm{C}$ :

$\mathrm{SiO}_2(s)+2 \mathrm{C}(s) \longrightarrow \mathrm{Si}(l)+2 \mathrm{CO}(g)$

Next, solid silicon is separated from other solid impurities by treatment with hydrogen chloride at $350^{\circ} \mathrm{C}$ to form gaseous trichlorosilane $\left(\mathrm{SiCl}_3 \mathrm{H}\right)$ :

$\mathrm{Si}(s)+3 \mathrm{HCl}(\mathrm{g}) \longrightarrow \mathrm{SiCl}_3 \mathrm{H}(\mathrm{g})+\mathrm{H}_2(\mathrm{~g})$

Finally, ultrapure Si can be obtained by reversing the above reaction at $1000^{\circ} \mathrm{C}$ :

$\mathrm{SiCl}_3 \mathrm{H}(g)+\mathrm{H}_2(g) \longrightarrow \mathrm{Si}(s)+3 \mathrm{HCl}(g)$

Silicon has a diamond crystal structure. Each cubic unit cell (edge length $a=$ $543 \mathrm{pm}$ ) contains eight $\mathrm{Si}$ atoms. If there are $1.0 \times$ $10^{13}$ boron atoms per cubic centimeter in a sample of pure silicon, how many Si atoms are there for every B atom in the sample? Does this sample satisfy the $10^{-9}$ purity requirement for the électronic grade silicon?

Solution

VerifiedThe problem asks to determine the ratio of silicon and boron atoms in a sample of refined silicon given the dimensions of its unit cell and number of boron atoms, as well as if the sample meets the purity requirement of $\mathrm{10^9}$ $\mathrm{Si}$ atoms per $\mathrm{B}$ atom.

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