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17 January, 11:04

In the manufacturing of computer chips, cylinders of silicon are cut into thin wafers that are 3.00 in. in diameter and have a mass of 1.50 g of silicon. How thick, in millimeters, is each wafer if silicon has a density of?

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  1. 17 January, 11:22
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    Answer: thickness h = 0.014cm

    Question: In the manufacturing of computer chips, cylinders of silicon are cut into thin wafers that are 3.30 inches in diameter and have a mass of 1.50 g of silicon. How thick (mm) is each wafer if silicon has a density of 2.33 g/cm 3? (The volume of a cylinder is V=πr 2 h)

    Explanation:

    The volume of a cylinder is

    Volume V = πr^2h ... 1

    The density of a material is

    Density D = mass m / volume V

    D = m/V ... 2

    Since m and D are given, we can make V the subject of formula.

    V = m/D ... 3

    From equation 1, we need to derive the thickness h of the cylindrical silicon.

    h = V/πr^2 ... 4

    Substituting equation 3 into 4

    h = (m/D) / πr^2 ... 5

    Given.

    mass m = 1.50g

    density D = 2.33g/cm^3

    radius r = diameter/2 = 3.00in/2 = 7.62/2 cm = 3.81cm

    Substituting the given values into the equation

    h = (1.5/2.33) / (π * 3.81^2)

    thickness h = 0.014cm
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