The Alpha Particle : Part 4 : Inside the Earth

The Field Guide to Particle Physics
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The definitive resource for all data in particle physics is the Particle Data Group: https://pdg.lbl.gov.

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A few References and Resources for you.

Isotopes of Helium:
https://en.wikipedia.org/wiki/Isotopes_of_helium

Helium Fact Sheet from NIST:
https://webbook.nist.gov/cgi/inchi/InChI%3D1S/He

CDC Fact sheet on Uranium-238:
https://www.cdc.gov/nceh/radiation/emergencies/isotopes/uranium.htm

US Information Agency Facts on Energy Consumption:
US : https://www.eia.gov/energyexplained/us-energy-facts/
World : https://www.eia.gov/todayinenergy/detail.php?id=49876

Berkeley National Lab Essay on Earth's Heat
https://newscenter.lbl.gov/2011/07/17/kamland-geoneutrinos/

The Alpha Particle
Part 4 : Inside the Earth

Density

Helium, Neon and Argon are all noble gases. None of them react to form chemicals. As the chemists are fond of saying, their electron valence shells are filled.

So why is Helium such a scare resource, while Argon in particular makes up a sizable fraction of our atmosphere?

In a word, Density.

Helium is much less dense a gas than Neon or Argon. With only two protons and two neutrons, helium is about ten times less dense then the air we typically breathe on Earth.

Just like air bubbles under water, balloons full of helium rise in the atmosphere because they’re less dense than the surrounding media.

Something similar can be said about heavy things. Rain falls from the sky when water vapor condenses to form droplets of liquid water. That liquid is much more dense than the air around it, so it falls. All the way down. To Earth.

A similar thing happens INSIDE the Earth. It’s a little less intuitive because rocks and dirt are typically solid. But denser material tends to sink towards the center of the earth. Of course, that sinking takes place on geological time, not human time.

Really heavy elements, like Uranium and Thorium aren’t terribly common up near the surface of the Earth. But inside. There’s quite a bit of both. And we’re very lucky that is so.

Helium Creation
Deep in the Earth, Uranium and Thorium decay. They’re radioactive, and as we discussed last time, they occasionally decay by spitting out an alpha particle. An alpha particle, you might recall, is nothing but a Helium nucleus.

That alpha particle eventually soaks up a couple of electrons from the surrounding environment, turns to helium and begins to rise, literally, through the cracks. It eventually pools in underground wells, as discussed in part two of this series.

This is a long process, and not just because it takes a while for the Helium atoms to migrate up to those subsurface wells. The real bottleneck is alpha decay. In some sense, its a pretty uncommon event. A typical Uranium-238 nucleus lives for about 4.5 billion years. And each event only produces ONE helium atom.

Helium Production Rate
Trying to build an intuition for atoms and molecules is difficult because they’re so small. They are so small AND there are so many of them.  What does it mean to say that a typical MRI machine might go through a million billion billion helium atoms in a given year?

Frankly, I’m not sure, but it’s a lot. Especially considering how long it takes for a Uranium nucleus to decay. The reason we have any helium around at ALL is because we have SO MUCH URANIUM in the earth.

Rather than attempt to wildly estimate the rate at which helium is produced deep underground, it’s better to explain that uranium lifetime - that 4.5 billion years -  a bit more precisely.

In part three of this series, we explained that alpha decay was a random sort of thing. It was a “quantum tunneling event” - as physicists are fond of saying. It’s not guaranteed to happen at any given point in time. But it happens at a typical rate. For uranium 238, that’s about once every 4.5 billion years.

But that framing is a bit misleading.

When folks say that uranium-238 has a typical lifetime of 4.5 billion years, they are usually referencing its “half-life”. And the “half-life” is a technical term used by scientists to model the decays of radioactive elements. But it’s pretty easy term to understand.

The half-life of an isotope, like uranium-238, is the time it takes for HALF of the material to decay. So in 4.5 billion years - about the age of the earth - half of the uranium-238 present today will decay to thorium-234. For each one of those decays, we’ll get a new atom of helium.

You might see now, how helium is such a nonrenweable resource. In some sense, about HALF of all the helium we could ever get from uranium-238 has already been formed. And in the next 4.5 billion years, we’ll only get HALF of that half, more.

While we don’t really know how much that is, it’s still a pretty sizable amount. The really challenging part, which we discussed in part two, is getting the helium that’s LEFT out of the ground.

Heat
Every time a nucleus decays underground, energy is released. A good chunk of that energy goes into the motion of the ejected particle, like the alpha particle. Those particles bounce around in the Earth’s mantle and crust, banging into all kinds of other atoms, distributing that energy around.

Those kinds of atomic collisions are what we talk about when we talk about heat.

Heat is nothing other than the motion of individual atoms. If it’s a fluid - like helium gas - that heat amounts to the actual kinetic energy of the individual atoms. If it’s a solid, its more of the vibrational energy of the individual atoms shaking together.

Nuclear decays contribute a LOT of heat to the Earth.

Physicists have estimated the annual heat radiated by all radioactivity of Uranium and Thorium to be about 20 trillion watts. It’s a bit like comparing apples to oranges, but this value isn’t that far from the 17.7 trillion watts of electrical power consumed by humanity in 2020.

That’s a LOT of heat, and we feel the effects of all that heat all the time.

Geothermal Power

Radioactivity isn’t really keeping you warm at night. Not unless you’re sitting in a geothermal hot spring, perhaps near Yellowstone National Park. Light and other radiation from the SUN does most of the warming of our planet’s surface and the atmosphere.

But INSIDE the earth is  another matter. Physicists estimate that about HALF of the Earth’s internal heat is driven by radioactive decay. That’s a tremendous amount of heat.

Heat being heat, flows. It tries to warm up colder things. The heat from inside the Earth - where temperatures are measured in the 1000s of degrees - flows towards the surface.  Sometimes it pops out: volcanic eruptions, geysers and steam vents are common all around the Earth.

The intense heat inside the Earth is...