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QUESTION

# If I have a chart that claims that the Atomic radius of Rubidium is 248 picometers cubed, how can I calculate how many Rubidium atoms span the length of 1.00 centimeter (Assume that the Rubidium atoms are touching each other) ?

2.02 * 10^(7)"atoms of Rb"

For starters, the atomic radius of rubidium cannot be expressed in picometers cubed, "pm"^3, because that is a unit used for volume, not for length.

My guess would be that you're indeed dealing with the atomic radius of rubidium, which is equal to "248 pm".

If that's the case, the first thing to do here would be to convert the desired length, i.e. 1.00 centimeters, to picometers. To do that, go from centimeters to meters first, then from meters to picometers

1.00 color(red)(cancel(color(black)("cm"))) * (1color(red)(cancel(color(black)("m"))))/(10^2color(red)(cancel(color(black)("cm")))) * (10^(12)"pm")/(1color(red)(cancel(color(black)("m")))) = 1.00 * 10^(10)"pm"

So, you know that the radius of a rubidium atom is equal to "248 pm". The thing to look out for here is the fact that you need to use the diameter of an atom, which is you know is equal to

color(purple)(bar(ul(|color(white)(a/a)color(black)("diameter" = 2 xx "radius")color(white)(a/a)|)))

The diameter of a rubidium atom will thus be

"diamter" = 2 xx "248 pm" = "496 pm"

Now all you have to do is figure out how many atoms would fit in that length

1.00 * 10^(10)color(red)(cancel(color(black)("pm"))) * "1 Rb atom"/(496color(red)(cancel(color(black)("pm")))) = color(green)(bar(ul(|color(white)(a/a)color(black)(2.02 * 10^7"atoms of Rb")color(white)(a/a)|)))

The answer is rounded to three .