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Silicon used in computer chips must have an impurity level below 10910^{-9}. Silicon is prepared by the reduction of quartz (SiO2)\left(\mathrm{SiO}_2\right) with coke at about 2000C2000^{\circ} \mathrm{C} :

SiO2+2C(s)Si(l)+2CO(g)\mathrm{SiO}_2+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 350C350^{\circ} \mathrm{C} to form gaseous trichlorosilane (SiCl3H)\left(\mathrm{SiCl}_3 \mathrm{H}\right) :

Si(s)+3HCl(g)SiCl3H(g)+H2(g)\mathrm{Si}(s)+3 \mathrm{HCl}(g) \longrightarrow \mathrm{SiCl}_3 \mathrm{H}(g)+\mathrm{H}_2(g)

Finally, ultrapure Si\mathrm{Si} can be obtained by reversing the above reaction at 1000C1000^{\circ} \mathrm{C} :

SiCl3H(g)+H2(g)Si(s)+3HCl(g)\mathrm{SiCl}_3 \mathrm{H}(g)+\mathrm{H}_2(g) \longrightarrow \mathrm{Si}(s)+3 \mathrm{HCl}(g)

(c) Silicon has a diamond crystal structure. Each cubic unit cell (edge length a=543pma=543 \mathrm{pm} ) contains eight Si\mathrm{Si} atoms. If there are 1.0×10131.0 \times 10^{13} boron atoms per cubic centimeter in a sample of pure silicon, how many Si\mathrm{Si} atoms are there for every B\mathrm{B} atom in the sample? Does this sample satisfy the 10910^{-9} purity requirement for the electronic grade silicon?

Question

Silicon used in computer chips must have an impurity level below 10910^{-9} (that is, fewer than one impurity atom for every 109Si10^9 \mathrm{Si} atoms). Silicon is prepared by the reduction of quartz (SiO2)\left(\mathrm{SiO}_2\right) with coke (a form of carbon made by the destructive distillation of coal) at about 2000C2000^{\circ} \mathrm{C} :

SiO2(s)+2C(s)Si(l)+2CO(g)\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 350C350^{\circ} \mathrm{C} to form gaseous trichlorosilane (SiCl3H)\left(\mathrm{SiCl}_3 \mathrm{H}\right) :

Si(s)+3HCl(g)SiCl3H(g)+H2( g)\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 1000C1000^{\circ} \mathrm{C} :

SiCl3H(g)+H2(g)Si(s)+3HCl(g)\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=a= 543pm543 \mathrm{pm} ) contains eight Si\mathrm{Si} atoms. If there are 1.0×1.0 \times 101310^{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 10910^{-9} purity requirement for the électronic grade silicon?

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The 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 109\mathrm{10^9} Si\mathrm{Si} atoms per B\mathrm{B} atom.

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