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## Lab: Size of an Aluminum Atom

### Introduction

In this brief 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 (cm3).
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. Use this percentage to 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. Divide the total volume by the number of atoms.
6. Atoms are modeled as small, hard spheres. Use the formula for the volume of a sphere to find the radius of an aluminum atom (V = (4/3)πr3 so use r = ∛(3/4·V/π)). Report your answer in cm.
7. Find the diameter of an aluminum atom in centimeters.
8. 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. You have already measured L and W and calculated the volume: use the volume based on the density from the first step.
9. 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.
10. Convert the radius of an aluminum atom from cm to pm.
(pico- is the prefix for units at 10-12 from the base unit so 1 cm = 1 x 1010 pm).
11. The actual radius of an aluminum atom is 143 pm. What is the percent difference between your result and the actual radius? What might explain the difference? (Percent difference is calculated using the absolute value of the difference between your measured result and the standard value. Divide this difference by the standard value and multiply by 100%.)
12. How closely did you follow the steps of this calculation? This sequence of calculations makes a logical error by assuming the answer in advance. If you can identify the steps in the calculation that produced this error then your teacher may offer you some extra credit!
The idea for this activity is due to Nathan Guerin. The writing was all done by Aaron Keller. Last updated: Mar 22, 2024       Home