Determining the Radius of an Aluminum Atom
Introduction
In this lab activity you will measure the length, width and mass of a piece of aluminum
foil. You will use these data to calculate the thickness of the foil (see also the density lab
from earlier in the year). Next, you will calculate the size of an individual aluminum
atom. Finally, you will calculate the thickness of the aluminum foil in aluminum atoms.
This activity is designed to give you practice with measurement, dimensional analysis,
simple geometry, and the mole concept. Incidentally, you will need to use skills in
scientific notation and the metric system.
Procedure
1. Obtain a piece of aluminum foil and cut it to be a perfect rectangle. The size of
the piece of foil does not matter except that if its length is the length of the carton
its width should be no less than 15 cm.
2. Measure the length and width of the rectangle to the nearest hundredth of a
centimeter and record the information below.
3. Find the mass of the rectangle of aluminum foil to the nearest hundredth of a
gram and record the information below.
Length (cm)
Width (cm)
Mass (g)
Questions and Calculations
1. Use the density of aluminum metal (2.70 g/cm3) to find the volume of aluminum in
your rectangle. Report the result in cubic centimeters.
2. Atoms of a metal are spherical and so do not take up all the space in the
material. Think of how oranges pack in the display at the supermarket: there are
spaces between the oranges and there are spaces between the aluminum
atoms. The amount of empty space in your piece of metal is about 25.9% of the
total volume. So the aluminum atoms take up 74.1% of the volume. Find the
volume of all of the aluminum atoms combined.
3. Find the number of moles of aluminum metal in your rectangle using the mass
you measured and the molar mass of Aluminum.
4. Find the number of atoms of aluminum metal in your rectangle using the number
of items in a mole.
5. Find the volume of a single aluminum atom now that you know the total volume
of all the atoms combined and how many there are.
6. Atoms are modeled as small spheres. Use the formula for the volume of a sphere
to find the radius of an aluminum atom (V = 4/3πr3).
7. Convert the radius of an aluminum atom from cm to pm (pico- is the prefix for
units at 10-12 from the base unit).
8. Find the diameter of an aluminum atom in centimeters.
9. Find the thickness of your aluminum foil in cm. This can be accomplished using
the formula: V = L × W × H. Solve for H (height), which is the thickness.
10. Calculate how many atoms of aluminum there are in the thickness of the foil now
that you know the diameter of a single atom and the thickness of the foil in cm.
11. The true radius of an aluminum atom is 143 pm. What is the percent error
between your result and the actual radius? What might explain the difference?
12. Do the experiment again, but this time with copper. Make sure copper has it’s
own data table.The density of copper is 8.93g/cm 3. Also, assume that only about
75% of the copper is occupied by atoms. The remainder is empty space.
13. The true value for the radius of copper is 128pm. Calculate your percentage of
error.
14. Describe the errors that could have or did occur in this experiment.