Gold, which has a mass of 19.32 g for each cubic centimeter ofvolume, is the mos

Question

Gold, which has a mass of 19.32 g for each cubic centimeter ofvolume, is the most ductile metal and can be pressed into a thinleaf or drawn out into a long fiber. (a) If a sample of gold, with a mass of77.36 g, is pressed into a leaf of2.800 µm thickness, what is the areaof the leaf?
1 m2

(b) If, instead, the gold is drawn out into a cylindrical fiber ofradius 1.000 µm, what is the lengthof the fiber?
2 m (a) If a sample of gold, with a mass of77.36 g, is pressed into a leaf of2.800 µm thickness, what is the areaof the leaf?
1 m2

(b) If, instead, the gold is drawn out into a cylindrical fiber ofradius 1.000 µm, what is the lengthof the fiber?
2 m

Explanation / Answer

mass of each cubic cm is m = 19.32 g Mass of gold M = 77.36 g Volume of the gold V = ( M / m ) * 1 cm ^ 3                                  = 4.00414 cm ^ 3                                  = 4.00414* 10^-6 m ^ 3 Thickness t = 2.8 * 10 ^ -6 m Area of the leaf   A= V / t                             = 1.43 m ^ 2 (b). Radius r = 1 * 10 ^ -6 m we know V = r^2 * L from this length L = V / r ^ 2                           = 1.274 * 10 ^ 6 m

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