I love gold. Do you love gold? I think everyone loves gold!

It is common enough for everyone to have a little bit of it, but rare enough to hold its intrinsic value. Gold doesn’t tarnish, oxidize, or interact much with other elements at all; it is very stable. In fact, Gold is the heaviest known ‘monoisotopic’ element, meaning that 100% of all naturally occurring gold comes in just one form: the perfectly stable Au-197 isotope. That’s the main reason why I love gold!

Stable elements, such as Gold (Au-197), are those which have no tendency to "decay", i.e., change into another element.

Unstable elements, on the other hand, have isotopes that decay from one state to another – and this is the basis of radioactivity.

The dictionary definition of radioactivity is “The emission of ionizing radiation or particles caused by the spontaneous disintegration of unstable atomic nuclei.”

Ok, that’s quite a mouthful. But note that wording which says “spontaneous disintegration” of the atomic nuclei. Spontaneous disintegration happens instantly. At one point in time, there is an atom – and then suddenly you have a different atom (or a different isotope) and an emission of ionizing radiation (i.e., the “radio activity”).

The point in time for any disintegration is completely indeterminate. We can never know exactly when any individual atom will decay. However, we can absolutely say, from a statistical standpoint, how many atoms will decay in a specific time period, and that time period is called the “Half-Life” of the element.

The half-life is the time that it takes for half the atoms in any given sample to decay. It doesn’t matter if you have just a few hundred atoms, or trillions upon trillions … half of them will decay in the period of that element’s half-life.

In *Figure 1* below, let’s assume each “X” and “O” represents a billion atoms. Half of the remaining “unstable atoms” will decay in the passing of each half-life:

*Figure 1*

Interestingly, some elements have a half-life of just a few billionths of a second and some have a half-life in the billions of years.

While it’s true that we have absolutely no way of knowing when any one individual atom will spontaneously decay, the measurement of “exactly half the atoms will decay in ‘x’ period of time” is exceedingly accurate and very consistent. The half-life of any isotope can be calculated from the atomic structure, and the measurement of the half-life matches the calculated values to within many parts per billion. In fact, it’s turned out to be far more accurate than the resolution tolerance of our best measurement devices – so by default, quantum decay has now become our new standard for measuring time.

The atomic Master Clock at the United States Naval Observatory in Washington DC (which uses cesium and rubidium as the decay elements, and hydrogen masers for measuring the decay) has an accuracy of 0.000 000 000 000 000 007 seconds. This is the clock that satellites use for ensuring a stable orbit around the Earth, and what your GPS uses for determining its location based on radio signals triangulated from the satellites’ exact position. Without such precise and accurate clocks, these systems would not function.

In my previous article “The Quantum Quandary”, I talked about the quantum effect of electrons pushing against the junction of a transistor – without the absolute precision of quantum mechanics, the microprocessor you are using right now to read this article (which probably has some 6 billion transistors turning on and off at a rate of some 3 billion times a second) would not run for more than a few seconds without crashing.

There is no doubt that the intricate equations that define the physics of quantum mechanics are highly accurate.

By measuring the ratio of the original element and the resulting element from radioactive decay, you can calculate the age of things like rocks and fossils. The concept is simple enough but let’s take a closer look at the steps it takes to get there.

Organic material, as the simplest example, can be dated using “radiocarbon” techniques. This is based on an unstable isotope, Carbon-14, which decays into a stable isotope of Nitrogen – specifically Nitrogen-14. There are three naturally occurring isotopes of carbon on Earth: Carbon-12 and Carbon-13 (both are stable elements), and then Carbon-14 (which is only found in very small trace amounts as described below).

The dating process is based on the following assumptions:

• Carbon-14 is a radioactive isotope that is created in plants during photosynthesis. It not known to be formed by any other means.

• Carbon-14 is ingested by animals when they eat the plants. When both plants and animals die, some amount of Carbon-14 stays in the cells.

• Carbon-14 decays into Nitrogen-14 with a half-life of 180,701,003,776 seconds (5,729.991 years).

• Nitrogen-14 does not occur naturally, the only way it gets created is through the radioactive decay of Carbon-14.

• Nitrogen-14 is a stable isotope that does not decay further into yet another atomic form.

• We can collect enough Carbon-14 and Nitrogen-14 to precisely measure the amount of both elements in a sample.

• The age of the sample can be calculated with a standard formula: Age = half-life * log (amount of Carbon-14 / amount of Nitrogen-14) / log 2

Obviously, if any of these points turn out to be incorrect, we will get incorrect results. However, each step has been independently studied and verified, and the entire process stands up to full scientific rigor and scrutiny. Admittedly, the collection and measurements of the sample is subject to ‘human error’.

There is an upper limit to the age that can be measured using this technique. As you can see in *Figure 1* above, there comes a point in time when there is just not enough of the original element left to get an accurate measurement. For Carbon-14 dating, the upper limit is about 60,000 years (just a little over ten half-lives). Remember that there are only “trace amounts” of Carbon-14 produced during photosynthesis to begin with, and my sixth bullet point states that we need to collect a large enough sample of BOTH Carbon-14 and Nitrogen-14 to get an accurate measurement.

The process for determining the age of inorganic materials (rocks, etc.) is based on similar logic – but instead of Carbon-14, other radioactive decay chains are used (Uranium–Lead, Samarium–neodymium, Potassium–argon, Rubidium–strontium, etc.). Most of these have longer half-lives and the elements are more abundant – which provide accurate measurements at longer timescales than we can get with Carbon-14. However, some of these interactions are more complicated as the initial element does not decay directly to a stable element, so there are ‘intermediate’ elements and secondary decay chains that need to be considered.

An unstable element is said to be “Radioactive”, because as the element decays, it emits energy in the form of radiation (typically alpha particles, beta particles, neutrinos, or gamma rays). Some of these forms of radiation can be quite dangerous, even with moderate exposure.

So, here’s a simple question: when an atom ‘decays’, is the resulting atom heavier or lighter than the original one?

As you may have already surmised, the resulting element will **always** be lighter than the original. Radioactive decay converts mass into energy; since mass is ‘lost’ in this conversion process, the resulting atom is lighter.

The energy that is released can be very precisely calculated by taking the DIFFERENCE between the atomic weight of the original atom and the resulting atom, and multiplying it by the speed of light squared … or put another way, E (energy) equals m (difference in mass) time c^{2} (speed of light squared).

You should be familiar with the famous equation, E=mc^{2}; radioactive decay is just one practical example of how it can be applied to the real world.

The equation E=mc^{2} is a ‘ratio’ of the mass to energy and is stated without any specific units; mass and speed of light can be in in either metric or English (or other) units. The ‘ratio’ will still apply – but typically E (Energy) is in Joules, m (mass, typically written lower case) is in kilograms, and c (Speed of Light, also notated in lower case) is meters per second. (be careful, as physicists will sometimes use shortcut units that need further conversion – it’s like saying “Olympia is an hour south of Seattle” when we all know that an hour is not a unit of distance).

In particle physics, the ‘mass’ is equivalent to the molecular weight of an atom. So, while the mass of an individual atom is quite small (a hydrogen atom weighs just 1.67 x 10-24 grams) to get the total ‘potential energy’ of the atom you multiply that by the speed of light, squared. In metric units the speed of light is 299,792,458 meters per second … and when that value is squared, you get an impressively large number: 89,875,517,873,681,764.

You might be thinking that a single kilogram of Uranium-235 (the element most often used for nuclear power) would produce 89,875,517,873,681,764 joules of energy then, right? After all, Energy (in Joules) = 1 (mass in kg) times 89,875,517,873,681,764. Converting from Joules, this would be 24.97 TRILLION Watt-hours. That means we can just about satisfy humanity’s annual energy consumption with just one kg of U-235!

Unfortunately, as mentioned above, you need to look at the DIFFERENCE between the original mass and the resulting mass – and in the case of fission reaction, the resulting mass is the nuclear waste which is produced. When we use equation E=mc^{2} we really have to apply it as E = (m_{1} – m_{2}) * c^{2} (where m_{1} is the original mass and m_{2} is the resulting mass after the reaction). And we can never ‘capture’ 100% of the energy that was produced. So in practical terms, 1kg of U-235 provides about 8.64x10 13 joules, or 24 gigaWatt hours of energy. Still, that’s very impressive compared to 1kg of coal (which produces about 8 kWh of usable energy), or mineral oil (approximately 12 kWh from 1 kg).

There’s a key point here that you need to understand. Converting the entire mass of an atom into energy requires complete and total destruction of the atom – and the only known way to achieve this is with a matter/antimatter interaction, which results in “mutual annihilation”.

Antimatter, unfortunately, is exceedingly difficult to come by. Extremely small amounts are created within stars and it can be found in cosmic rays. Antimatter can be produced artificially – so far, about 20 nanograms (billionths of a gram) have been made by humans, and the individual molecules must be held in a “penning trap” … a container using magnetic fields in a perfect vacuum; this is to prevent the antimatter from touching air, since air is made of matter.

But E=mc^{2} is not only used for radioactive measurements … this formula applies any time that matter is converted to energy!

For example, if you burn a log in a fireplace, you are converting mass into energy. You may not realize it, but the total weight of the soot and smoke that is carried into the air is almost as heavy as the log was before it was burned! The total energy (light and heat) produced by burning the log can be calculated by measuring the difference in the weight of the log, and the weight of the remaining ashes, soot, smoke, non-combustible minerals, and water vapor emitted. You would be very surprised to find that the difference in weight is very small, almost immeasurable. According to FirewoodResource, a full cord of white oak weighing 1700 kg produces 24 million BTU’s of energy when burned. Per E=mc^{2}, this released energy results in a material weight loss of just 0.000000272 kilograms.

This concept also applies to burning gasoline in cars – which is why reducing automobile pollution is such a difficult problem. Up until the early 1970’s, the exhaust from a car’s engine was directly expelled into the air. A typical car manufactured in the 1960’s (before pollution control devices) discharged 520 pounds of hydrocarbons, 1,700 pounds of carbon monoxide, and 90 pounds of nitrogen oxide for every 10,000 miles traveled. As with our example with the burning log, the total ‘weight’ of all that exhaust is very close to the weight of the gas that went into the car.

This is still the case today, but through exhaustive research (if you’ll pardon the pun) we’ve been able to create technologies that capture, filter, neutralize, and ‘convert’ (i.e., a catalytic converter) the emissions so that they have far less impact on our environment. We’ve gone to unleaded gas. We’ve developed more efficient engines that have better mileage, and made cars lighter so they need less energy to move – all these advancements mean we burn less gas and produce less automobile exhaust, which is toxic and highly damaging to our environment. We’ve made tremendous progress on reducing emissions per mile driven, but people are driving more miles on average now – so it’s still a huge problem.

If you think about it, you will see that wind, solar, geothermal, hydroelectric, tidal, and all other ‘green’ energy sources really have just one thing in common: they convert one form of energy into another form of energy, rather than converting matter into energy. That’s it! You can convert sunlight, heat, kinetic motion, and pressure (all forms of energy) into electricity without creating any byproducts.

Extracting energy from coal, radioactive material, oil/gasoline, or firewood will always produce nearly the same amount of waste – pound for pound – as fuel consumed. The conversion itself is very efficient due to E=mc^{2}, but only a minutely small amount of fuel actually gets converted into energy, the rest is converted to by-products, which are almost always toxic.

And note that while a gas engine directly converts fuel to kinetic energy (to move a car), a nuclear power plant converts matter to heat first and THEN converts the heat to pressure (in the form of boiling water) and then pressure to electricity like in a hydroelectric dam. It’s a multi-step process.

E=mc^{2} tells us that energy is matter and matter is energy; they are really two different forms of the same thing and can be converted back and forth. It doesn’t matter if the conversion is from an unstable element that naturally decays due to radioactivity, nuclear fuel forced into a fast chain reaction, or fossil fuel burned for heat. The difference between the original mass and the resulting mass will always tell us how much matter has been converted, and how much energy was produced. And E=mc^{2} even tells us how long ago the dinosaurs lived before they became the fossil fuel we are burning to run our cars.

Are we good now? I think we’re good as gold!

June 27. 2018 08:24

Finally, an essay on these topics that I can understand! Thanks for this piece, David, which manages to be clear, instructive, thought-provoking, and entertaining. I doubt I will ever look at a burning log the same way again...

Tom Welsh

June 27. 2018 13:46

Exceptionally good explanation! I've read many articles on various physics topics and they are all WAAAAYYY over my head. Great to have someone break it down into bite sized chunks that all make perfect sense. Your definition of 'green energy' is spot on, very simple and concise. I had never thought of it that way before but you are absolutely correct.

B.Markel