Calculating the size of an atom using very little…
You will be taking a variety of measurements of a piece of metal to determine the size of the atom for that
element in the metal. You need to make sure all measurements and calculations have a UNIT.
You will need:
A ruler
A calculator
A balance
A metal strip or piece of foil
First, select a metal strip and write down the element’s symbol here: _______________
Second, measure the length and width of the strip and calculate the area: ________ x ________ = ________
This number will be used later.
Third, determine the mass of your metal strip on a balance: ________
Fourth, you will calculate the volume of the strip by using the published density. To do this, look in the
appendix of a chemistry book and find the alphabetical list of elements. The density is: ________
Now that you have the density, and you have the mass, you can determine the volume of your strip using the
density formula of D  m . The volume is: ________
v
You can also calculate the thickness of the strip without using a ruler. V  l  w  h and h is also the same as
thickness, t. A  l  w so you can get the formula V  A  t and use the calculated area and volume to find t.
Okay, now enough fooling around with that! Time to calculate the atomic size. First you need to find the
atomic mass of your element and round it to the nearest hundredths place. The atomic mass is :________
Atomic mass gets the unit a.m.u. for atomic mass unit.
Now, if you were to have 6.02 x 1023 atoms of any element, you would have a mass in grams equal to the
atomic mass and the a.m.u. unit could be changed to grams. 6.02 x 1023 is known as the Avogadro Number and
we will deal with it more in a later chapter. You can determine how many atoms you have in your strip with
23
this number by using the mass of the strip like this: mass  1mole atomic  mass  6.02  10 1mole  atoms
Your answer should have an answer with an exponent of positive 20 to 23. Your answer is: ________________
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The volume of an atom can be calculated by doing this: volume  atom  volume  strip
number  of  atoms
The volume of one of the atoms in your strip is: ________________. This should be a number with a negative
exponent between negative 20 and negative 23.
Atomic size is unfortunately not expressed in volume but in radius so this is what you need to do. The formula
for the volume of a sphere is V  4 r 3 so if the formula is rearranged to solve for r, then it becomes
3
3  V  of  atom
putting this in a calculator is annoying so do this by finding the math function 3 x then
r3
4
type the following in this order: ((3 x V)4 x 3.14)) <enter>. You should get an answer with an exponent of
negative 8. The radius is: ________________ and this would be ________________ in nanometers.