# A question on radioactive decay

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I was reading how earths core is heated by radio active decay and I was wondering if someone picked up a piece of uranium or plutonium that let's say the USA was Making a nuke from would it be hot to the touch? Isn't it mined for? If someone touched the raw material would it feel hot. If so how hot?

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The activity of U is low (U-235 has a half-life of around 700 million years), so it probably wouldn't be hot to the touch. For shorter-lived isotopes, like with Pu (half-life around 90 years), the answer could be yes: some spacecraft use the heat from decay and thermoelectric devices to generate electricity.

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Uranium-238 has Decay Energy 4.27 MeV

4.27 MeV is 6.84*10^-13 J

To heat 1 gram of water for 1 C you need 4.1855 J of energy.

4.1855 J / 6.84*10^-13 J = 6.12*10^12 atoms of Uranium-238 would need to decay to detect increase of temperature of 1g water for 1 C. That amount is 1/100,000 of 1/1,000,000 of mole.

But U-238 is quite stable.

Half-life is 1.41*10^17 seconds (nearly 4.5 billion years).

If you have 1 kg of pure U-238 now, you will have 500 grams of U-238 after 4.5 billion years (and other products of decay), and 250 grams after 9 billion years.

Some time ago, I have made application for calculating quantity of decays per second:

Unpack ZIP, and load it to OpenOffice, and enter in the second row Initial Quantity of unstable atoms and Half-Life in seconds. They will be spread to the all below rows. And show decays per second and graph.

Unfortunately 1.41*10^17 seconds is too much for OpenOffice to handle it (math issue of application).

But in second example I used 1.41*10^14 seconds (1/1000 less) (=~4.5 million years half-life)

and 1 mole of Initial Quantity (6.022141*10^23).

Result shows that there is approximately ~3 billions per second decays.

So for 4.5 billion years half-life there will be ~3 millions per second decays.

You would need to wait nearly 576 hours to heat 1 g of water for 1 C if you would have 238 grams of Uranium-238.

Energy in the core of Earth has nowhere to go, so it will add up.

Half life calculations.zip

Edited by Sensei

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I was reading how earths core is heated by radio active decay and I was wondering if someone picked up a piece of uranium or plutonium that let's say the USA was Making a nuke from would it be hot to the touch? Isn't it mined for? If someone touched the raw material would it feel hot. If so how hot?

Uranium is a lithophile element: it is chemically inclined to enter into rock forming minerals. There is practically no uranium in the core. Moreover, its preference for minerals common in the crust, along with the cyclic nature of vulcanicity and plate tectonics means that it has become concentrated in the crust and depleted in the mantle. (At least the upper mantle.)

Most of the radioactive heating of the mantle arises from decay of potassium isotopes that are relatively common in the mantle.

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Uranium is a lithophile element: it is chemically inclined to enter into rock forming minerals. There is practically no uranium in the core. Moreover, its preference for minerals common in the crust, along with the cyclic nature of vulcanicity and plate tectonics means that it has become concentrated in the crust and depleted in the mantle. (At least the upper mantle.)

Most of the radioactive heating of the mantle arises from decay of potassium isotopes that are relatively common in the mantle.

There appears to be some disagreement on this, I'm not sure which side to go with...

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The activity of U is low (U-235 has a half-life of around 700 million years), so it probably wouldn't be hot to the touch. For shorter-lived isotopes, like with Pu (half-life around 90 years), the answer could be yes: some spacecraft use the heat from decay and thermoelectric devices to generate electricity.

Pu239 has a half life ~ 24000 years.

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Pu239 has a half life ~ 24000 years.

Swansont was talking about Pu-238 ,

Half-life 87.7 years

http://en.wikipedia.org/wiki/Plutonium-238

"Plutonium-238 is a very powerful alpha emitter and – unlike other isotopes of plutonium – it does not emit significant amounts of other, more penetrating and thus more problematic radiation. This makes the plutonium-238 isotope suitable for usage in radioisotope thermoelectric generators (RTGs) and radioisotope heater units – one gram of plutonium-238 generates approximately 0.5 watts of thermal power."

"This same RTG power technology has been used in spacecraft such as Voyager 1 and 2, Cassini–Huygens and New Horizons, and in other devices, such as the Mars Science Laboratory, for long-term nuclear power generation."

Pu-238 is a good test for verification of mine previous calculations of decays per second in post #3.

87.7 y half-life = 2,767,601,520 seconds

1 gram of Pu-238 = 6.022141e+23 / 238.049553 =

2529784628497080000000 atoms.

Enter that in OpenOffice SpreadSheet Initial Quantity and Half-Life,

and we're receiving decays per second = 633,585,795,072

Each decay is releasing 5.593 MeV, which is 8.959986e-013 Joules.

8.959986e-013 * 633,585,795,072 = 0.5676919854 Joules per second

(article mentioned 0.5 Watts)

Pretty close.

Edited by Sensei

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There appears to be some disagreement on this, I'm not sure which side to go with...

Herndon has been publishing stuff on this for years. He is in a sub-set of one. He may be right, but his idea has failed to gain any traction among geophysicists. He's equivalent to the 0.5% of scientists who deny AGW, except his view is not dangerous.

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For having carried both a stone of uranium ore and a part of depleted uranium, I can tell they're cold (and damned dense for the metal). But 238Pu (which is not the isotope used for fission) glows red hot if insulated a bit, check the picture at wiki about RTG. Other nuclides, used for instance by medicine for imagery and therapy, are even much more radioactive, but never in big amounts.

Mined for: no, U is sought as a fissile element, more precisely its 235U isotope. This is not much related to radioactivity. Other nuclides would be much more radioactive, including natural ones. Or fission waste, which is more radioactive than uranium but can't fission any more. As for plutonium, it's not mined (only traces of natural plutonium exist on Earth), but produced at uranium reactors from 238U.

Exploiting heat from natural U or Th isn't economical, not even directly at the mine. It's being done from fission waste, but that's a serious risk for very little energy.

Uranium is a lithophile element: it is chemically inclined to enter into rock forming minerals. There is practically no uranium in the core.

Uranium will preempt oxygen and leave iron and nickel reduced. But does this suffice to leave the uranium in the mantle? U3O8 is a bit denser than both Fe and Ni and UO2 much more, so uranium oxides can sink, and then decompose to metal and oxygen at heat.

Is there any means to observe the composition of the core? I wish the coming neutrino observatories will detect radioactivity neutrinos as well, so they locate the nuclides in Earth.

Herndon's explanation of the geomagnetic field is less useful now that laboratory experiments could reproduce the dynamo.

Edited by Enthalpy

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Human knowledge has progressed thanks to Borexino, a neutrino detector at Gran Sasso, Italy. The paper is at Arxiv (thank you!), ref. 1506.04610v2

http://arxiv.org/abs/1506.04610

As I understand (or not) the paper:

• The detector is not directional.
• The team could discriminate neutrinos from nuclear reactors versus Earth beta radioactivity.
• They could infer a total beta radioactivity for Earth, from which alpha radioactivity and heat is deduced. This heat is consistent with the total terrestrial heat flux.
• The detector doesn't tell from measures where the terrestrial radioelements are located, and the deduced radioactive heat depends on the assumed radioelements distribution in Earth.
• From a pre-existing estimate of the radioactivity of the crust, the authors deduce that more radioactivity originates deeper.
• "Deeper" is written as "in the mantle" in the paper, but this may be influenced by dominant theories. Unless I missed something, the observations don't discriminate between the mantle and the core. Or do they?

Fantastic results. We know very little about the depth of our Earth. Most data is seismic and needs extensive interpretation to deduce some information. Here we have measures that rely less on models. I wish future experiments can refine the accuracy of the results, and (but how??) tell us some day where the radioactivity takes place.

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