Imagine a very heavy cube of pure gold that is 1.23 m on a side. Approximate the
ID: 2275156 • Letter: I
Question
Imagine a very heavy cube of pure gold that is 1.23 m on a side. Approximate the atoms in this cube as little cubes. The density of gold is approximately
. Its atomic number is 79, and its atomic mass is 197.0. The latin name for gold is aurum. The price of gold fluctuates, but approximate it as $50 USD/g.
Suppose all the little cubes in the expensive and heavy chunk of Au were lined up end to end. How far would the line stretch?
m
How long would it take a beam of light to travel from one end to the other of the line of atoms?
years
Explanation / Answer
Volume of the cube of pure gold=(1.23)^3=1.86 m^3=1.86*10^6 cm^3
density of gold given=19.3 g/cm^3
mass of the cube of pure gold=(19.3)*1.86*10^6=3.59*10^7 grams
atomic mass of gold=197 g/mol
no. of moles of gold =(3.59*10^7)/197 =1.823*10^5 moles
no .of atoms in the cube =(1.823*10^5)*6.023*10^23 =1.098*10^29 atoms of gold
if we approximate them as cubes and let the side of the cube be 'a' cm
then,
(1.098*10^29 )*(a^3) =1.86*10^6
a=2.568*10^-8 cm
so the side of each cube =2.56*10^-8 cm
if we line all the gold atoms then the line would stretch to a distance =(2.56*10^-8)*(1.098*10^29 )=2.82*10^21 cm
a)the distance the line would stretch =2.82*10^19 m
speed of the light=3*10^8 m/s
so time taken by light=distance/speed=(2.82*10^19)/(3*10^8) =9.399*10 ^10 s
time taken by the beam of light to travel from one end to the other of the line of atoms=2980.65 years