Copyright © Karl Dahlke, 2022

You reach into your lego box and pull out a piece you've never seen before. It is a standard brick, 2 dots by 4 dots, but it is bright orange, quite apart from the other pieces, which are white, red, yellow, blue, gray, and black. You turn it over in your hand and it looks normal. You attach some other bricks to it and the connections are solid. Yes indeed, this brick could be used to build a house, just like any other 2 by 4 brick. Pay no attention to its odd color. Suddenly, a particle shoots out the end, with a flash of light, and the brick transforms into a 2 by 3 brick, solid white in color. It is indistinguishable from the other 2 by 3 bricks in the box. It use to be an orange 2 by 4 brick, now it's a standard white 2 by 3 brick. It's also warm in your hand, as though it had released energy in the transformation. We thought lego blocks never changed. What gives?

If you had used this block to build a lego house, it would suddenly transform, and there would be a hole in the wall. That's not a big problem, but if too many blocks change, or if a critical load bearing block changes into a window or a slanted roof piece, that's a problem!

Atoms are eternal, or so Democritus thought, and that is almost always true, but there are some cases, some exceptions, where an atom can decay into another atom. Such an atom is called radioactive. Let's look at an example.

Element number 53 is iodine, with 53 protons and 53 electrons, and (usually) 74 neutrons. This is a stable atom that lives forever. However, there is an unstable isotope, iodine 131, with 78 neutrons, that is radioactive. A neutron can, without notice, separate into a proton and an electron. The electron flies out of the nucleus at high speed, leaving 54 protons and 77 neutrons. This is a xenon atom, xenon 131, and it is stable. It is not radioactive any more, and it is, for all practical purposes, eternal. An unusual isotope of iodine has transformed into a stable isotope of xenon. One element has changed into another. An orange lego block has become a different white lego block.

A neutron has no charge, but you can think of it as a proton and an electron merged together into one particle. At times we talk about a massive star squashing protons and electrons together. This analogy is both helpful and inaccurate at the same time. A neutron is a single particle, it isn't a proton and an electron dancing together. However, there are occasions where neutron ⇔ proton + electron. Notice that the charges balance, zero on either side, suggesting another scientific principle, conservation of charge.

When I-131 decays, a neutron turns into a proton, and the atomic number increases by one, from 53 to 54, from iodine to xenon. Magnesium 23 decays by the reverse process. A proton spits out a positron, a positively charged particle, leaving a neutron behind, as the conservation of charge demands. The atomic number decreases by 1, from 12 to 11, from magnesium 23 to sodium 23, which is stable.

In alpha decay, the nucleus spits out a piece of itself, a chunk consisting of 2 protons and 2 neutrons. This decreases the atomic number by 2. Finally, a nucleus can split in half, with each piece carrying off the electrons it needs to become a stable atom. One atom has become two, in a process called nuclear fission, from the Latin fissiōn, to split. All of these processes release energy - far more energy than a conventional fire.

Half Life

Watch an iodine 131 atom for 8 hours, and the odds are 50% that it will decay during those 8 hours. Thus iodine 131 has a half life of 8 hours. You can't determine that by watching one atom, but if you watch a million atoms, and 500,000 have decayed in 8 hours, then statistics tells you the half life is 8 hours. If the half life were 7 hours, it is almost impossible that fully half of the atoms would still be there after 8 hours. This is an application of a theorem called The Law of Large Numbers. Every radioactive element has a half life, which is experimentally determined by watching a large amount of atoms and seeing when they decay. The half life could be a fraction of a microsecond, or a billion years.

Suppose you start with 64 pounds of iodine 131. (You can use kilograms or ounces or tons or any unit you like.) After 8 hours half of the iodine has turned to xenon, leaving 32 pounds of I-131 behind. After another 8 hours half of the remaining iodine, half of the 32 pounds, has decayed, leaving 16 pounds. By the end of the 24 hour day there are 8 pounds remaining. After 2 days there is just one pound. After 3 days there is an eighth of a pound, or 2 ounces. After a week you'd have a hard time finding even a trace of iodine from your original sample.

Atoms have no memory. They don't know how long they've been around. If an iodine 131 atom is still around after 8 hours, it's like it just came into existence. It still has a 50% chance of decaying in the next 8 hours. And if it survives those 8 hours, it still has a 50% chance of decaying in the next 8 hours. Every hour, every minute, every second, every microsecond, each atom has a probability of decay that has nothing to do with the past.

As an exercise in exponential math, how much iodine is remaining in 4 hours? More than half, because half the iodine is still there after 8 hours. If the ratio after 4 hours is r, then the remaining iodine, which has no memory, is multiplied by the same ratio r during the next 4 hours. Therefore, r times r is ½, and r is about 70%. (0.7 times 0.7 = 0.49, which is about ½.) You might have guessed 75%, halfway between 50% and 100%, but you want the geometric mean, not the arithmetic mean, thus 70%. You could back this up and determine how much iodine remains after one minute, or even one second. I'll skip those calculations.

You might be wondering, if I-131 decays in 8 hours, how can there be any on earth? As it turns out, we know how to make it in the lab, and it has many uses in industry and in medicine. You can read about iodine 131 here.

Wherever I-131 is needed, it must be manufactured on site. Shipping it across the country next-day air doesn't help, because seven eighths of it is gone by the time the customer receives it. Besides, the U.S. postal service isn't thrilled about transporting radioactive materials.


The particles that spew out of a decaying atom are hazardous to humans, and just about all life on earth. There is a small amount of background radiation that we all tolerate, but larger doses of radiation should be avoided. This is not an issue for most of us, but it is a concern for some who work with these materials on a regular basis, or for individuals who live near a radiation spill such as Chernobyl or Fukushima.

The dangers were not known at the outset. Having isolated and discovered radium, an element that is so radioactive it practically glows in the dark, Marie Curie was happy to carry tubes of it in her pocket. It's really quite pretty, after all. She developed leukemia, and died soon thereafter. Still unaware of the danger, the radium girls painted radium onto watch dials an faces so they would glow in the dark, well into the 1930's. The real dangers of radiation were not understood, until the atomic bombs were dropped on Japan in 1945. some of the immediate survivers developed radiation sickness within a few weeks, while others contracted cancer several years later. Even nuclear tests high in the stratosphere, during the Cold War, spread small yet detectable amounts of radioactive material across the western states and Russia, which led to the atmospheric test ban treaty of 1963. Nuclear weapons have been tested underground ever since, where the radioactive fallout can be contained.

Nuclear Fission, Radioactive Decay, and Heat

Radioactive decay is energetically favored, thus it always produces heat. The amount of heat depends on the reaction and the amount of material. Heat and radiation are maximal at the start, and taper off exponentially. Return to our 64 pounds of I-131. A lot of atoms are decaying at the start, sending out high energy beta and gamma rays and producing heat. Eight hours later the radiation and heat production is cut in half, since half as many atoms are decaying. Eight hours later the energy is cut in half again, and so on. If there was a radioactive accident near you, it seems like you could hide in your home for a few days and all would be well, and in some ways that's true, but (A) your house is not air-tight, and (B) some radioactive elements remain hot for several years. This is the biggest long-term challenge to nuclear power, what to do with all that radioactive waste, that remains dangerous for 100,000 years.

In one oversimplified paragraph, a nuclear reactor has, at its core, an unusual amount of radioactive uranium, gathered together in concentrations not found in nature. Atoms fission through a chain reaction, wherein one atom splits and sends out particles which cause other nearby atoms to split. The resulting cascade produces heat, lots of heat. Heat can always be turned into electricity; we know how to do that whether the heat comes from burning coal, or natural gas, or the fission of unstable uranium atoms. On paper, the case for nuclear power is compelling, even before we had to worry about carbon emissions and global warming. One kilogram of uranium contains 3 million times as much energy as one kilogram of coal. That's not chump change! Traincars and traincars and traincars of coal can be replaced with a couple pounds of uranium. But the devil is in the details. The chain reaction is hard to control, and if it gets out of hand, the uranium melts, perhaps right through the cement floor of the power plant and down into the water table. This is where we get the word meltdown, which has also come to mean a complete loss of emotional control, crying and sobbing, and believe me, I've had a few of those. The other problem is the nuclear waste, after the uranium has released its energy. The byproducts remain radioactive for thousands of years, and we're still not sure what to do with them. Still, 3 million to 1 is a compelling ratio, as we try to chart our energy future. We've managed fire for half a million years, but we've never seen energy like this! It also explains why a nuclear bomb is a million times more powerful than a conventional bomb. That's the dark side of our species.

NASA uses radioactivity to generate electricity on its deep space missions, outside the orbit of Mars, where the sun does not provide enough power. These are passive materials that simply decay; they are not nuclear reactors with chain reactions that must be controlled. The device is called a radioisotope thermoelectric generator, or RTG for short, and it is simplicity itself, with no moving parts. The isotope of choice is plutonium 238, with a half life of 87.7 years, longer than any of our space missions to date. Even after 87 years, the RTG is still generating half its power, and the mission could continue with a few instruments turned off. Voyagers I and II are approaching 50 years of service and are still transmitting scientific data back to earth. NASA must work hand in hand with the Department of Energy to maintain a steady supply of Pu-238. It is difficult to manufacture, even in small amounts. As of March 2015, a total of 35 kilograms (77 pounds) of Pu-238 was available for civil space use.

Pu-238 becomes U-234 by alpha decay; here is a depiction. The alpha particle is flying off to the right. You may recognize the alpha particle from the last chapter as a helium nucleus. Quite a few isotopes decay in this way.

Simulated plutonium nucleus, without enough protons and neutrons Alpha particle

Natural Clock

A radioactive atom decays at a certain rate, which is part of the laws a physics. A manmade clock has mechanical flaws, it doesn't always run at the same rate, and sometimes it stops altogether. Your heart beats fast or slow, depending on a dozen different variables. Even chemical reactions depend on temperature. Thus a decaying atom is a perfect test of time dilation, as predicted by Einstein. Not one atom of course, since it could decay now or a year from now, but a thousand atoms, enough to provide a statistical sample. There are situations in which time itself slows down. The clocks don't run slower, chemical reactions don't run slower - time itself slows down. Your heart would beat slower, and your thoughts would slow down accordingly. Of course you would perceive time as you always have, but I would wonder, from my perspective, “Why are you moving so slowly, why are you talking so slowly, why is your heart beating so slowly.” We can't put a human into any of these situations, but we can subject a few thousand radioactive atoms to time dilation. The half life is lengthened in accordance with Einstein's formula. The theory is correct. These changes in time could be the most counterintuitive scientific discovery of the 20th century, yet they have been confirmed by our tiny radioactive clocks, and a hundred other experiments. We'll explore this topic later.