If the radius of a gold atom is 166 pico-metres than how many gold atoms would it take to fill a gold penny?

Answer 1

Dear Chelsea M.,

First of all, in your question, it's "then", not "than", you should have used.

So the information you need to collect to answer this:

1) gold has never (as far as I know) been used to make pennies. Therefore, what type of penny is the basis for calculation (several countries call their low-denomination coin a penny)?

2) Obtain dimensions of chosen penny type: either measure with calipers, or do a water-displacement measurement yourself (of many pennies, obviously)

3) Find the crystal structure of gold metal. This will tell you how the gold atoms use up space. You need to know this, because different stackings (packings) may have different bulk densities!

4) Note that you are (implicitly) NOT allowed to look up the density of gold directly; since you are given a radius. If you think your teacher wants you to *assume* a packing type, you could "assume" face-centered cubic, with reasons to justify!

-- Hope this points you in the right direction, -- Mr. d.

Answer 2

First, let's find the volume of a penny, that is: 4.42 * 10^--7 m3

Next, let's write out picometres in mathematical notation, which is: 166 * 10^--12 m

Let's convert the picometres into m cubed: 166 * 10^--12 cubed = 4.574 * 10 ^ -30 m3, this is the radius cubed.

We then use the equation for the volume of a sphere 4/3pi*r^3, to find the volume of the atom, so that's 4/3pi (4.574*10^--30) we already cubed the radius of the gold atom in the previous step. That = 1.9159 * 10 ^-29 m3.

Then we'll divide the volume of the penny by the volume of the gold atom:

That's 4.42 * 10^--7 m3 / 1.9159 * 10 ^-29 m3 = 2.307 * 10 ^22 atoms.

There are 2.31 * 10 ^22 gold atoms in a gold penny, with 3 significant figures.