Einstein's Energy

Energy equals mass times energy squared or e = mc^2. I think I can remember seeing that equation before I even knew what an exponent was. I didn't know what it meant, but it seemed important. Most everyone has seen it. My guess is that most, including students, don't really understand it, though.

Part of its beauty is not just that it is important, but you would think something this important would be a little bigger. It's really rather small as equations go.

Here are some fun facts about the equation.

• Giving off energy corresponds to a loss of mass. E = mc^2 tells us how much.
• The correct labels must be used. Being from Europe, Einstein used metric measurements.
• E is measured in Joules, m in kilograms, and c the speed of light, which is 300,000,000 meters per second.
• This formula was discovered by Einstein in 1905
• Chemical reactions, such as burning coal or wood are such that for the energy released, mass is lost, but it is almost immeasurable. Because of this, the formula wasn't physically shown to be true until 1932 - 27 years after Einstein's discovery.
• Einstein did not win a Nobel Prize for this or, for that matter, anything he did with relativity. He won it for the photoelectric effect.

There are a number on interesting problems students can work out that use this equation and a knowledge of scientific notation and rules of exponents. 

For example, The first atomic bomb released approximately 10^12 joules of energy. How much matter does that correspond to?

The matter in this case was Uranium-235. Using e = mc^2,

 10^12 = m(3x10^8)^2 gives approximately 0.000011 kilograms of mass.