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 4.981 g, is pressed into a leaf of 4.178 μm thickness, what is the area of the leaf? (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.400 μm, what is the length of the fiber?
Gold density = 19.32 g/cc
a) mass of gold m = 4.981 g
Volume V = m/ = 4.981 /19.32 =
0.2578 cc
thickness of leaf = 4.178E-6 m = 4.178E-4 cm
mass per sq.cm = 4.178E-4 *19.32 = 8.0719 E-3 g
Total mass of the sample = 4.981 g
Area of the gold leaf = 4.981/8.0719E-3 = 617.08 sq.cm
b) gold wire radius r = 2.4E-6 m= 2.4E-4 cm
volume of gold per m length = (2.4E-4)2
*100 = 1.81E-5 cc
mass of wire per 1m = 1.81E-5 *19.32 = 3.496E-4 gm
length of gold wire from 4.981 gm of gold = 4.981/3.496E-4
= 1.425E+4 m = 14.25 km
Gold, which has a density of 19.32 g/cm3, is the most ductile metal and can be...
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