Question

the radius of a gold atom is 1.35 angstroms. how many gold atoms would it take to line up a span of 8.5 mm?

Answer 1

Answer: Hello there!

We know that one millimeter is equivalent to 10^7 angstroms

then 8.5 mm is equal to 8.5x10^7 angstroms

Now we know that the radius of a gold atom is 1.35 angstroms, and we want to know how many gold atoms would take to line up a span of 8.5mm (or 8.5x10^7 angstroms)

First, the interval of distance that each atom would need in the line, is equal tho the diameter of the atom (assuming that there is no space between the atoms)

And the diameter is equal to two times the radius, so D = 2*1.35 angstroms = 2.7 angstroms.

So the amount of gold atoms needed to line up a span of 8.5 mm, is the number of times that 2.7 "enters" in 8.5x10^7

this is (8.5x10^7)/2.7 = (8.5/2.7)x10^7 = 3.15x10^7

Then there are 3.15x10^7 gold atoms in a line of 8.5 mm.

Answer 2

The angstrom, also known as the angstrom unit, is a measure of displacement equal to 0.0000000001 meter (10 -10 m). It would be helpful to convert the units of angstrom to mm. We do as follows:

diameter = 2 x 1.35 x10^ -10 m ( 1000 mm / 1 m ) = 2.7 x 10^-10 mm / atom

Number of gold atoms = 8.5 mm / 2.7 x 10^-10 mm / atom = 31481481481.481 atoms