Human Life and Radioactivity.

People with only a smattering of modern scientific knowledge are aware that the Sun's energy comes from nuclear reactions.

This is the more remarkable in that Lord Kelvin concluded from thermodynamics that the Earth and the Sun could not possibly be as old as the age that biologists (Darwin et al.) and geologists (Lyell et al.) insisted upon for the Earth. His estimate was that its age was more than twenty million, but less than a hundred million years.
It was Kelvin who deduced the existence of absolute zero temperature, thus inventing the scale of temperature now named after him(1)

The biologists needed hundreds, or more likely thousands, of millions of years for animals to evolve from micro-organism ancestors. The geologists needed such ages for the chalky deposits of marine skeletons at the bottom of the seas to become compressed into chalk, then limestone and marble, and then lifted up to become the peaks of the Alps and the Himalaya.

What Kelvin didn't know about was radioactivity and Einstein's mass-to-energy equation. Nuclear reactions convert tiny amounts of mass into astonishingly large amounts of energy.(2)

Hydrogen's atomic weight is about one, and Helium's is four. To four decimal places, the figures are

So when four nuclei of hydrogen inside the Sun successively collide to form one of helium, there is a net loss of slightly less than one percent of the total mass involved. This mass is converted into various forms of energy, and eventually emerges from the Sun's surface, mostly as radiation. The Earth captures a tiny fraction of what the Sun loses, and most living things on Earth make use of it.

In the Carboniferous era, solar energy was trapped photosynthetically and became coal beds after some considerable geological activity. For every 12 tons of carbon laid down in this way, the atmosphere received 32 tons of oxygen, which is equally of photosynthetic origin! If we burn the carbon, and sequester the carbon dioxide (an improbable hope) the atmosphere loses that oxygen. It is believed by most chemists and physicists that the origin of petroleum and natural gas is the same. These are called fossil fuels. A few astrophysicists, pointing out the abundance of methane in Jupiter's huge atmosphere, think it possible that much of Earth's methane could be as old as the planet itself. But if so, there would not be enough oxygen in the atmosphere to burn it!

But besides that, the existence of life itself on Earth required a process of evolution. Kelvin accurately showed that the physics then known would require that the Earth was molten only a few tens of millions of years ago. A hundred million years is not long enough for the first paleo-invertebrate's descendants to have branched out into sharks, mice, frogs, snakes, birds and humans. The vocabulary of the DNA code translates words of three 'letters' of the code into one of the amino acids that synthesize into proteins. The same vocabulary is identical for ALL living organisms on this planet, which fact by itself proves common ancestry for apes, pigs, humans, snakes, fish, trees, kelp, cyanobacteria, yeasts, fungi, pathogenic bacteria, symbiotic bacteria, compost-heap bacteria, and even the weird archeo-bacteria that live in geyser ponds and tectonic sea-bottom vents. Including those to whom oxygen is a poison.

So what keeps the Earth molten? From what do the forces of continental drift come? What drives the volcanoes, and lifted the Rockies and the Himalaya?

Radioactivity! --Ancient, very long-lived, primordial energy that was stored long before the Sun existed.

When the Sun has converted all its hydrogen to helium, its mass will be about one percent less. But that is a catastrophic loss! Sir Arthur Eddington showed that the forces which hold up a star against the pressure of its own gravity are dependent upon the high temperature of the plasma (ionized gas) of its interior. His results showed that a very massive star must be disproportionately hotter than a smaller one. Relativity showed that mass to energy conversion could fuel a nuclear furnace. So when the blue giants of the Pleiades, which are burning up much faster than the Sun, run out of fuel, they will go into gravitational collapse.(3)

Our relatively small Sun is more frugal, and will last longer, several more thousands of millions of years. In a very large star, the gravitational collapse heats it to very high temperatures for a while, and much more violent nuclear reactions take place. This is not so much because the available nuclear reactions supply more energy than the premium hydrogen-to-helium one, but because of the violence of conversion of gravitational energy to nuclear!
Even on Earth, it has been calculated that a meteorite, big enough to blast a crater like the largest craters known upon Earth, must have not only vaporised, but in fact ionised the atoms involved, and would emit x-rays like an atomic bomb.
The nuclei are propelled at each other in a chaotic falling, crowded mess that is driven by the remaining gravitational energy of huge masses crashing together.
In this confusion, there is enough excess energy in some of the collisions to create nuclear masses in a way that absorbs energy. Every element that has a nucleus more massive than iron must have come into existence in some such conditions.(4)
The energy stored in any of these elements includes a fraction of the gravitational energy that caused the collapse of a star.

So, if you insist, radioactive potassium, thorium, and uranium are fossil fuels. But they come from before the birth of our Sun. The Earth is between four and five thousand million years old. The half-lives of these radio-isotopes are comparable. So we may deduce that the newly-solidified Earth had about twice as much Uranium-238 as it does now. It must have had about 30 times as much U-235, because U-235 has a significantly shorter half-life of 703.8 million years. Radioactive potassium, K-40, has 1300 million year half-life.


  1. Kelvin scale

    Kelvin's temperature scale is fundamental in science. It is ridiculous to quote the Sun's temperature in Fahrenheit, and pointless even to use Celsius for it. A temperature of 600 Kelvin is exactly twice as hot as 300 Kelvin. There is no such thing as below-zero Kelvin. The efficiency of a heat engine (steam, internal combustion, gas turbine) is best understood in terms of the absolute temperatures in its working cycle.
  2. Nuclear Reactions convert Mass to Energy

    Strictly speaking, so do chemical reactions, but when you divide the energy of the explosion of a ton of TNT by the square of the speed of light, the difference in mass is so small as to be undetectable. That's why there were two conservation laws, one for matter and the other for energy, for so long. Now it's known that the sum of the two is conserved.
  3. Blue Giant Stars

    They're believed to be a few hundred million years old as of now.
  4. Supernovae

    Or, conceivably, even more violent processes not long after the Big Bang.

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