Question

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 1.891 g, is pressed into a leaf of 5.173 μm thickness, what is the area of the leaf? (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.900 μm, what is the length of the fiber?

Answer 1

(a) Density= 19.32 g/cm^3

So, mass/ volume= density

Or, 1.891/ (area*thickness)= 19.32

Or, 0.0978= area* 0.0005173cm

So, area of the leaf= 189.21 cm^2

(b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.900 μm= 0.00029 cm, then

So, mass/ volume= 1.891 g / (area * length) = 19.32

So, 0.0978=  π*0.00029^2*length

So, length = 370427.9cm= 3704.279m

So, length of the fiber is = 3704.279m

please upvote when understood to appreciate