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 3.245 g, is pressed into a leaf of 3.989 ?m thickness, what is the area of the leaf? (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.700 ?m, what is the length of the fiber?

Answer 1

a) Density = mass/vol So vol = mass/density = 3.245/19.32 = 0.16796066 cm3

vol = Area X thickness, so Area = vol/thickness

Firstly, 3.989 micrometres = 3.989 X 10^(-6) = 3.989 X 10^(-4) cm

Area = vol / thickness = 0.16796066 / 3.989 X 10^(-4) cm

= 420.90 cm^2

B) vol of cyl = pi X r X r X length = 0.16796066 cm^3 from above

r = 2.700 micrometres = 2.7 X 10^(-4) cm3

length = (0.16796066)/(2.7 X 10^(-4) X 2.7 X 10^(-4) X 3.14)

= 3.245/19.32x 3.14 x (2.7x10-4)2

=733753.8cm
  
=7.33754km