Einstein’s famous equation tells us that mass and energy are in fact equivalent, opening the door to a new era in energy production and sadly, unthinkable levels of destruction. Not only is the “stuff” which makes up your body actually just concentrated energy, a single atomic nucleus holds a staggering amount of power. One of the best ways to understand the devastation that occurred at Hiroshima and Nagasaki is to do the calculation for yourself and see what results you get. It’s also elegantly simple, serving as an excellent example of how equations can be used to describe the natural world.
- Skill level:
- Moderately Easy
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Things you need
- Scientific calculator
Put it into language you understand. Don’t let the equation scare you; the letters in it are simply used to represent difficult values. It actually stands for “energy equals mass times the speed of light squared.”
Learn the scientific units used. In SI (the International System of Units), mass is defined in kilograms (kg), energy is quantified using joules (j) and speed is described in metres per second (m/s). Your result will be an amount of energy in joules.
Find out how heavy the subject of the equation is. You can calculate the amount of energy any amount of matter contains using the same simple equation. Remember that you need to get the mass in kg. Just use 1kg if you want to make things easier, but you could also see how much energy is contained within your body, within a single book, or anything you like!
Switch on your calculator or use an online option (see Resources – or type “scientific calculator” into Google). Type in your weight (remember that if it’s less than a kg you’ll need to use decimal values – one gram is 0.001 kg) and press the multiply button. Enter the speed of light. You can use 300,000,000 m/s if you like, but it’s technically 299,792,458 m/s, so that will yield more accurate results. Just type the numbers; the units of speed (m/s) are just there for reference. Press the “squared” button, which is usually an “x” followed by a “2” in super-script.
Press “=” to find the answer in joules. If you calculated 1kg, the answer is 89,875,517,873,681,764 j for the more accurate speed of light and 90,000,000,000,000,000 j if you used the simpler figure (which is ordinarily used for calculations).
Compare this to other power usage to give yourself an idea of how much energy that can be produced. For example, it’s been calculated that running a desktop computer and a monitor for four hours a day throughout an entire year uses 394 kilowatt-hours worth of energy. A kilowatt-hour is equivalent to 3,600,000 joules, so in total you’ll use around 1,418,400,000 joules of energy to power your computer all year. Dividing the energy contained within one kilogram of mass by this figure gives a result of over 63 million. This means that if everybody in the UK had a desktop computer and monitor on for four hours per day, one single kilogram would be able to provide the power for an entire year.
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