Can One Ounce of Gold Really Be Pulled into a 50km Wire?

[kassib]

Homework Statement

one ounce of gold (taken to be 28.35g) can be pulled or drawn into a monofilament wire that can be up to 50km in length

true or false

support your argument with some evidence

Homework Equations

atomic mass of gold ,Au= 196.96
avagardo's number=6.02x10²³ atoms/mole
approx. radius of a single gold atom r=10^-10 m
volume of sphere=4XpieXr³/3

The Attempt at a Solution

one ounce of gold X atomic mass ?

 

[berkeman]

Homework Statement

one ounce of gold (taken to be 28.35g) can be pulled or drawn into a monofilament wire that can be up to 50km in length

true or false

support your argument with some evidence

Homework Equations

atomic mass of gold ,Au= 196.96
avagardo's number=6.02x10²³ atoms/mole
approx. radius of a single gold atom r=10^-10 m
volume of sphere=4XpieXr³/3

The Attempt at a Solution

one ounce of gold X atomic mass ?

Welcome to the PF!

What is the volume of 1oz of gold? What is a reasonable diameter for a thin monofilimanet wire? What would the volume be of such a wire at the length asked about in the question?

 

[kassib]

a reasonable diameter for the monofilament could be 0.25? work out the volume of this and times and times the answer by 50 ?

 

[berkeman]

a reasonable diameter for the monofilament could be 0.25? work out the volume of this and times and times the answer by 50 ?

0.25 what, for goodness sake?!

And you don't multiply volume by distance to get volume again...

 

[rwisz]

number of atoms in one ounce of gold = ? number of moles of gold

= 28.35g X 196.96 g/mol = 5587.86 atoms of gold

To form a monofilament wire, these atoms must be arranged in a single line, with each atom touching the next. Assuming that the radius of a single gold atom is 10^-10 m, the total length of the wire would be:

5587.86 atoms X 10^-10 m/atom = 5.58786 X 10^-6 m = 5.58786 micrometers

This calculation shows that it is not possible to create a gold wire that is 50km in length from one ounce of gold. In fact, even if we were to use all the gold in the world (estimated to be around 190,000 tons or 171,500,000,000 grams), the maximum length of the wire would only be approximately 9,600 kilometers. This is still far short of the stated length of 50km.

Therefore, the statement that one ounce of gold can be pulled into a 50km monofilament wire is false. This is because the amount of gold in one ounce is not sufficient to create a wire that is 50km in length, based on the size of a single gold atom and the fact that the atoms must be touching to form a single line. This shows that the statement is not supported by scientific evidence and is likely an exaggeration or inaccuracy.