E=MC² Made Simple

I was hooked on science at a very early age by a television program called “Watch Mr. Wizard.” I wasn’t quite eight years old when Mr. Wizard aired on NBC for the first time on March 3, 1951, but I was precocious and had a very enquiring mind. Every Saturday morning, I sat on the floor in front of our old RCA console TV watching as Don Herbert explained what at first appeared to be an incomprehensible concept. He demonstrated those concepts using experiments that any young scientist could safely duplicate at home without causing mom or dad alarm. When the original series ended in 1965, I had become a Mr. Wizard in my own right.

Over the years I have taught adult education classes on everything from auto mechanics to photography and if I have learned anything from all my students, it’s-KISS (Keep It Simple Stupid)-and I’m going to attempt to employ that concept in explaining E=MC^2. For those of you who might not be familiar with the use of the carat (^) in this manner, the carat means that the numeral 2 is actually in a superscript position, or read as M squared.

One of Albert Einstein’s greatest contributions to the science of physics was the discovery that energy can be converted into matter and that matter can be converted into energy. He not only provided us with that concept, he provided us with a mathematical formula that enables us to calculate how much energy a given mass can produce.

A couple of definitions are in order at this point. What is energy? What is matter?

Energy may be defined as a system's ability to cause something to happen. The chemical energy stored in a battery causes free electrons to flow through the light bulb in our flashlights, heating the tungsten filament, causing it to give off light. In other words, the battery converts chemical energy into electrical energy. The electrical energy is then converted into heat and light energy by the bulbs filament. Energy comes in many forms-mechanical, chemical, electrical, thermo, light, nuclear, etc.

Matter is a much easier concept to define because matter is anything that takes up space and has weight. However, what confuses many people is the fact that matter doesn’t have to be visible to meet both of those requirements. Take subatomic particles, like electrons and protons. These particles are so tiny that we can’t see them even with the most powerful microscopes, yet they have weight and they take up space in every atom. It’s in relationship to the atom that the formula E=MC^2 is most closely associated but before I explain how it is used to calculate the amount of energy contained in one atom, let’s look at the variable “C” in the formula.

The variable “C” represents the speed of light in meters per second. Light travels at a rate of 299,792,458 meters per second. For most calculations we round that off to 3.00 X 10^8 meters per second. The speed of light is also equal to 1.86 X 10^5 miles per second. However, for this formula to work we have to work with the metric version. If the thought of working with formulas like this one sends shivers up and down your spine, you’re in good company. My wife has taught for over twenty-five years and has a dual certification in Spanish and French but she has to send our grand children to me for help with their math. Just for fun, I gave her an eighth-grade algebra test and she flunked with flying colors. Actually the formula E=MC^2 involves nothing more than multiplication but because we will be working with both very large and very small numbers we will have to employ the power of ten notation to make them more manageable.

In the formula E=MC^2, the M^2 is simply the speed of light in meters per second raised to the second power or 3.00 X 10^8 X 3.00 X 10^8 which equals 9.00 X 10^16. When working in powers of ten, or scientific notation, we multiply the coefficients (3.00) and add the powers (10^8 + 10^8 = 10^16).

To illustrate the use of this formula, let’s take a look at the simplest of atoms, the hydrogen atom. The hydrogen atom consists of one proton in its nucleus and one electron orbiting the nucleus. The hydrogen proton has a mass of 0.000 000 000 000 000 000 000 000 001 672 Kg or 1.672 X 10 ^-27 Kg.

How much energy does that proton contain? Let's use the formula. E=MC^2= (1.672 X 10 ^-27 Kg) (9.00 X 10^16) =15.048 X 10^-11 =1.5048 X 10^-10 Joules. One Joule isn’t a very large amount of energy. To get a better conception of how much energy is contained in one Joule, it is equivalent to the force exerted by an average size textbook striking the floor when dropped by a student. Think of it this way, if all the energy contained in all the oxygen and all the hydrogen atoms in one Kilogram of water was released at the same time it would be equal to the energy released by burning 10 million gallons of gasoline.

Just think, since 70 percent of the earth’s surface is water, wouldn’t it be great if we could develop a car that converted water into mechanical energy?

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Holly Berard
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Jerry Walch
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Jerry Walch
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Posted on Dec 13, 2008