|MadSci Network: Chemistry|
We must define first the meaning of lightness. One piece of metal may be lighter than other because it has less volume. In other words, it may be lighter because it is smaller or porous. People perceive aluminum lighter than iron because one usually holds metal pieces of similar size in the hands, and yes, aluminum is lighter than iron most of the time.
To be more precise, we should compare pieces of different metals with exactly the same volume, and this is called density. Densities are usually measured in grams per cubic centimeter although there is nothing wrong if we want to measure density in ounces per cubic inch. The idea is to use a unit of volume, and weight different materials of that same unit of volume. Let's stick with the more common grams per cubic centimeter or g/cm3. It turns out that aluminum (Al) has a density of 2.70 g/cm3 near room temperature while iron (Fe) has 7.87 g/cm3. In other words, a cubic centimeter of Al weighs 2.70 grams while one cubic cm of Fe weighs 7.87 grams. That's nearly 3 times heavier than Al for pieces of metal with identical volumes. We say that Fe is almost 3 times denser than Al. When speaking of densities, we must specify the temperature because most matter, specially metals and gases, expand with temperature. Therefore if we heat up a piece of metal, its density will decrease as its volume increases while its weight remains the same.
The next question to ask is why Al density is smaller than Fe. For this we need to understand how matter is composed. Matter is made up of atoms. An atom is the smallest piece of matter that will keep its chemical properties intact. If I keep dividing a piece of Al, I'll have to stop when I get a single atom if I want to retain something that is still Al. The density of a material thus depends on the weight of its individual atoms and how densely packed they are. Most metals have a crystalline structure. That means that their atoms are arranged in an ordered pattern that repeats itself over long distances within the material. Atoms keep a crystalline structure by bonds between them that keep the material together.
It turns out that Al atoms arrange themselves in a crystalline structure of face-centered cubes. That means that Al atoms form cubes, with an atom in each corner of the cube and an additional atom at the center of each face of the cube. The side of the cube measures 4.05 Angstroms. An Angstrom, abbreviated A, is about 4 billionth of an inch. Thus I have 14 Al atoms packed in a cube of 66.4 cubic A. Al atoms weigh 27 atomic mass units. An atomic mass unit, or amu, is 1.66 X 10-24 grams or 5.85 X 10-26 ounces. An amu is close to the weight of a hydrogen atom or more exactly one twelveth the weight of a carbon atom.
Fe atoms arrange themselves in body-centered cubes, which means that Fe atoms form cubes with an atom in each corner and an additional atom at the center of the cube. The side of the cube is 2.87 A for a total of nine Fe atoms packed in a cube of 23.6 cubic A. Fe atoms weigh 56 amu. You can see the face-centered cubes and body-centered cubes in the Wikipedia entry of the cubic crystal system.
Let's see if we have enough data so far. If I have 14 Al atoms, weighing 27 amu in a box of 66.4 cubic A, and 9 Fe atoms, weighing 56 amu in a box of 23.6 cubic A, how much more dense is Fe with respect to Al? If density is weight over volume, the weight of 9 Fe atoms is 1.3 times lighter than the weight of 14 Al atoms. But the 14 Al atoms are packed in a volume 224 times bigger than the 9 Fe atoms. That means that a Fe crystal cube is 1.33 X 224 = 3.8 times denser than an Al crystal cube, isn't it? We said that Fe was almost 3 times denser than Al, or 2.9 times to be more exact. Why the difference between 3.8 and 2.9. If you think it carefully, when we put together more cubes in the crystalline structure, some atoms take places in adjacent cubes. For example to form two Al cubes side by side, I don't need 28 atoms, but only 23, because I can use the five atoms of one side of one cube to form the next cube. How many atoms do you need to form an array of 27 cubes in a supercube of three by three by three smaller cubes? Give it a thought! The answer is 910 Fe atoms and 172 Al atoms. With these numbers I get that Fe is 3.09 denser than Al. Not a bad answer when compared with 2.9! To do an exact calculation we need to add more and more cubes, count atoms and volumes properly and compare with experimental measurements. That would be too hard work for today.
Better ask why Fe atoms are more tightly packed than Al atoms in a crystalline structure. Remember that atoms are formed of protons, neutrons and electrons. Protons and neutrons are concentrated in a very small region at the center of the atom called the nucleus. Electrons are distributed all over the space that forms the atom. Thus the electron distribution within the space of an atom determine how large the atom is and also the distance between atoms when two atoms bond together to form a crystalline structure. Calculating those distances are the work of heavy research in atomic physics, but we can have an idea from measured sizes. Al atoms have a radius of about 1.43 A, while Fe atoms have a radius of 1.26 A. That and other factors like the way electrons distribute themselves in the atom make Fe atoms get packed more tightly in a crystal than Al atoms, but this is well beyond of this answer. The weight of an atom on the other hand depends on the number of protons and neutrons. Electrons don't count on this because a proton or a neutron is 1836 times heavier than an electron. Naturally found 92% of Fe atoms have 26 protons and 30 neutrons in their nucleus, while almost all Al atoms in nature have 13 protons and 14 neutrons, and each proton and neutron weighs about 1 amu.
Vladimir Escalante Ramírez
Center for Radio Astronomy and Astrophysics
National University of Mexico
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