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Energy of Matter

Matter stores energy in a variety of ways. Sometimes it is stored as chemical energy, other times it is stored as mechanical or potential energy. These are all small when compared to the energy stored in the form of mass. The famous scientist, Albert Einstein, discovered the relationship between mass and energy. This relationship is given by E=mc $^2$ [energy=mass $\cdot$ (speed of light) $^2$ ]

Though this relationship is important, it is more useful when written as E= $\Delta$ mc $^2$ [energy= change in mass $\cdot$ (speed of light) $^2$ ]

This principle is the driving idea behind fission and fusion reactions. For fusion, two hydrogen atoms are fused to create a Helium atom. The mass of the two hydrogen atoms is slightly larger than the new helium atom. This small amount of mass is converted to energy.

To understand just how much energy is stored in matter complete the following:

Example: Suppose 0.5Kg of mass were to be converted to energy using fusion reactions. How much energy would this be?

(For reference 0.5Kg is larger than 1 pound)

(1 pound $\approx$ 0.045Kg)

Known	Find	Relevant equation
m=0.5Kg c=3 $\cdot$ 10 $^8 \frac{m}{s}$	Energy Produced	E=mc $^2$

plug in numbers E=0.5Kg $(3\cdot10^8 \frac{m}{s})^2$
solve E=4.5 $\cdot10^14$ J
The first atomic blast used in world war II was about $10^14$ J This means that 0.5Kg of matter contains 450 times the energy of the first atomic weapons.