The “Thickness” or Radius of a Metal Atom

Objectives
The student will:

• use principles of the scientific method to develop a procedure to determine the radius (“thickness”) of an Al atom
• perform the experimental procedure that s/he developed
• compare the results with published data

Materials

• aluminum foil
• copper foil/sheeting/tubing
• measuring ruler graduated in mm
• volumetric measuring device
• weighing device

Terms to research

• Atom
• Molecule
• The Mole
• Avogadro’s number
• Atomic number
• Atomic weight
• Volume of a sphere

Introduction
Matter that exhibits unique chemical properties is thought to be composed of small particles called atoms and molecules. The purest substances that are easily obtained are metals such as aluminum, copper, and tin. If we were to be able to look with a very powerful microscope, we would notice that each of these metals are made up of individual atoms and that each atom of a specific element has the same number of protons in the nucleus (atomic number). Each aluminum atom has 13 protons in its nucleus, each copper atom has 29 protons, and each tin atom has 50 protons. As the number of protons in the nucleus increases, the effective “thickness” of the atom increases. Avogadro (a famous chemist) suggested that 6.02 x 10²³ (10 taken to the 23rd power) atoms of any element weigh the same number of grams as the number of protons plus the number of neutrons (this is known as the atomic mass of an element). So, we would expect that this number of atoms (also known as a “mole”) of aluminum atoms to weigh 26.98 grams, a mole of copper atoms to weigh 63.55 grams, and a mole of tin atoms to weigh 118.71 grams.
Since we can directly determine the weigh of a sample of a pure metal, we can calculate the number of atoms of the metal in that sample, using the atomic weight. We can also determine the volume that the sample of the metal occupies. There are two generally used ways of determining the volume. One is by direct measurement of the dimensions of the metal sample or measuring the amount of water that the sample displaces. During the latter method, a known volume of water is placed in container that has volume measurement marks on it (such as a baby bottle, medicine measuring spoons, or a graduated cylinder). The metal is then placed into the water and the difference in the indicated volume is measured. The additional volume can be attributed to the space occupied by the sample. Within the volume of the metal sample, we know that only 78% is occupied by the actual atoms, because of the way that the atoms stack during the solidification of the liquid metal.
We can assume that the atoms are for the most part spherical in shape (little balls) and we know that the volume of a sphere is calculated by using the formula, V = 4.19r³. By calculating the difference in the volume of the sample and the volume actually occupied by the atoms in the sample, we can determine that volume occupied by each atom. Using this formula for the volume of a sphere, we can then calculate the radius of each atom. So, take the volume that you measured and multiply it by 0.78. This is the volume occupied by all of the atoms. To determine the number of atoms, divide the weight of the metal by the atomic weight of the metal. This number is the number of moles of atoms. Multiply the number of moles and 6.02x10²³. This calculation results in the number of atoms in your sample. Divide the volume by the number of atoms and the result is the volume per atom. The radius of the atom will be equal to the cube root of the volume per atom divided by 4.19.

Procedure
The purpose of this laboratory exercise is to have you develop a procedure to experimentally determine the radius of an aluminum (Al) atom and a copper (Cu) atoms. Then use the procedure to perform the experiment, collect your data, then complete the laboratory report.

Questions to the Answered

1. Describe the procedure that you developed to determine the radius of the atoms.
2. Calculate the volume of each metal sample. Show your calculations.
3. Calculate the numbers of atoms in each metal sample. Show your calculations.
4. Calculate the volume of each atom in each metal sample. Show your calculations.
5. Use the Internet to determine the actual radius of the atoms of each of the metals and compare your results with the published data.
6. Discuss where the error occurred during your experiment.