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Gold, which has a density of 19.32 g/cm3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (a) If a sample of gold with a mass of 7.158 g, is pressed into a leaf of 2.810 μm thickness, what is the area of the leaf? (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.600 μm, what is the length of the fiber?

Respuesta :

Answer:

area  of the leaf is 0.13167 m²

length of the fiber is 17431.1235 m

Explanation:

Given data

gold density = 19.33 g/cm3

gold mass = 7.158 g

thickness = 2.810 μm =  2.810 × [tex]10^{-6}[/tex] m

radius = 2.600 μm

to find out

area of the leaf and  length of the fiber

solution

first we calculate volume from density

we know density formula that is mass / volume

so volume = mass / density

put these value

volume = 7.158  /  19.33

volume = 0.370 cm³ = 0.370 × [tex]10^{-6}[/tex] m³

so area = volume / thickness

area = 0.370 × [tex]10^{-6}[/tex]  / 2.810 × [tex]10^{-6}[/tex]

area = 0.13167 m²

and

area of fiber is = πr²

so area =  π(2.600× [tex]10^{-6}[/tex] )²

area = 2.12264 × [tex]10^{-11}[/tex]

so length = volume / area

put value

length = 0.370 × [tex]10^{-6}[/tex] / 2.12264 × [tex]10^{-11}[/tex]

length is 17431.1235 m

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