Weighty Matters Involving Electrons
Have you ever wondered how much the electrons that power our car weigh?
As I was musing over the properties of our Tesla Roadster electric car the other day I was drawn to the single most massive component of our car which is the battery. This nearly 1000 pound system is composed of various chemicals, enclosures, and electronics to safely deliver high voltage electrons which we then direct to power our car. So the electrifying question is – how much do all those electrons weigh? In other words, if we could weigh each and every electron as it left the battery on its journey out to do useful work, what would be the total weight of all of the electrons combined? Of course the battery does not change weight because for every electron leaving the battery, one returns, having expended its useful energy in a most exciting and entertaining way.
Fortunately, all the conversion factors have already been calculated and we need merely to set up the parameters and run the numbers. We will start with a full charge and drain the battery of its theoretical capacity. In this case we will use 2.2 Ampere hour cells. Each brick in our battery is composed of 69 cells in parallel; this defines the Ampere hour capacity of our battery. The 99 bricks in series in our battery give us our voltage, but we will focus on the number of electrons flowing and disregard their Voltage potential.
69 cells times 2.2 Ampere hours per cell equals 151.8 Ampere hours.
By definition, a Coulomb of Electrons is equal to 6.24 times ten to the 18 electrons. This is the number of electrons that flow past in one second at a defined rate of one Ampere. This means that in one hour (3600 Seconds) 3600 Coulombs flow by at 1 Ampere. Since our battery is 151.8 Ampere hours we multiply 3600 Coulombs times 151.8 which is equal to 546,480 Coulombs. This is a lot of Coulombs, but it represents an even larger number of electrons. Each Coulomb is to 6.24 times ten to the 18 electrons. Thus 546,480 Coulombs times 6.24 x 1018 electrons per Coulomb equals 34.1328 times 10 to the 23rd electrons. Wasn’t that fun? Remember that number, 34x1023 Electrons are available for our use in the battery.
This is a huge number of electrons and now we can finish by multiplying by the weight of an electron. When I started this problem I knew that electrons are much lighter than the Protons or Neutrons that make up the rest of the atoms so I roughly figured that of our 1000 lbs of battery we would wind up with a few ounces or at least a few grams of Electron weight. Any guesses?
The actual weight of an Electron is 9.05 x 10-28 grams, that’s right, 9.05 times ten to the minus twenty eighth Grams, an incredibly small mass. Multiply 34.1328 x 1023 times 9.05 x 10-28 and we get 308.9 Grams times ten to minus 5 or in other words, 3.089 Milligrams of electrons. This is about as much weight as a single, small grain of sand. I was amazed at how light and yet powerful these electrons we work so hard to control are, and to imagine that by pushing this tiny amount of mass through our motor over a period of hours, the magnetic fields generated propel our Tesla Roadster 244 miles is simply - shocking.
Marty Taft is an Electrical Technician here at Tesla Motors, and is an avid baker in his spare time.