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Chapter 4: Problem 23

The concentration of \(\mathrm{P}\) in \(\mathrm{Si}\) is \(1.0 \times 10^{-7}\) at \(\%\). What is the concentration in kilograms of P per cubic meter?

Short Answer

Expert verified
Answer: The concentration of phosphorus (P) in silicon (Si) is approximately \(2.33 \times 10^{-3}\) kilograms per cubic meter.

Step by step solution

01

Find the mass fraction of P in Si

First, we need to find the mass fraction of P in Si. Since the concentration of P in Si is given in percentage, we can find the mass fraction by dividing the concentration by 100. So, the mass fraction of P in Si is \((1.0 \times 10^{-7})/100\).
02

Convert the mass fraction to a decimal

To convert the mass fraction to a decimal, simply divide it by 100: $$\frac{1.0 \times 10^{-7}}{100} = 1.0 \times 10^{-9}$$
03

Find the density of Si

The density of silicon (Si) is 2.33 grams per cubic centimeter. To find the density in kg/m³, we need to multiply the density by 1,000,000 (since there are 1,000,000 cubic centimeters in a cubic meter): $$\mathrm{Density \, of \, Si} = 2.33 \,\text{g/cm}^3 \times 1,000,000 = 2,330,000 \, \text{kg/m}^3$$
04

Calculate the mass of P in one cubic meter of Si

Multiply the density of Si by the mass fraction of P to find the mass of P in one cubic meter of Si: $$\mathrm{Mass \, of \, P} = 2,330,000 \, \text{kg/m}^3 \times 1.0 \times 10^{-9} = 2.33 \times 10^{-3} \,\text{kg/m}^3$$
05

Final Answer

The concentration of phosphorus (P) in silicon (Si) is approximately \(2.33 \times 10^{-3}\) kilograms per cubic meter.

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Most popular questions from this chapter

Molybdenum (Mo) forms a substitutional solid solution with tungsten (W). Compute the number of molybdenum atoms per cubic centimeter for a molybdenum- tungsten alloy that contains \(16.4 \mathrm{wt} \%\) Mo and \(83.6 \mathrm{wt} \% \mathrm{~W}\). The densities of pure molybdenum and tungsten are \(10.22\) and \(19.30 \mathrm{~g} / \mathrm{cm}^{3}\), respectively.

Gold (Au) forms a substitutional solid solution with silver (Ag). Compute the weight percent of gold that must be added to silver to yield an alloy that contains \(5.5 \times 10^{21}\) Au atoms per cubic centimeter. The densities of pure Au and \(\mathrm{Ag}\) are \(19.32\) and \(10.49 \mathrm{~g} / \mathrm{cm}^{3}\), respectively.

Calculate the unit cell edge length for an \(80 \mathrm{wt} \% \mathrm{Ag}-\) \(20 \mathrm{wt} \%\) Pd alloy. All of the palladium is in solid solution, the crystal structure for this alloy is \(\mathrm{FCC}\), and the room-temperature density of \(\mathrm{Pd}\) is \(12.02 \mathrm{~g} / \mathrm{cm}^{3} .\)

What is the composition, in atom percent, of an alloy that consists of \(5.5 \mathrm{wt} \% \mathrm{~Pb}\) and \(94.5 \mathrm{wt} \% \mathrm{Sn} ?\)

Electronic devices found in integrated circuits are composed of very high purity silicon to which hasbeen added small and very controlled concentrations of elements found in Groups IIIA and VA of the periodic table. For Si to which has been added \(6.5 \times 10^{21}\) atoms per cubic meter of phosphorus, compute (a) the weight percent and (b) the atom percent of P present.
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