By Stefan Kühn (Own work) [GFDL (http://www.gnu.org/copyleft/fdl.html), CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/) or CC BY-SA 2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/2.5-2.0-1.0)], via Wikimedia Commons

We can profitably harness radioactive uranium for power. Can we do the same with radioactive carbon?

Short answer: No.

Long answer: Without doing any math, my intuition says “no, carbon decay probably can’t be harnessed profitably.” As a general rule, if something can be done profitably, then someone is doing it. I call it the argumentum ad economicum, or the ideal gas law of economics. Industry expands to exploit all potential profit available to it.

Scientifically speaking, let’s just compare carbon-14 as a nuclear power source to uranium-235. The abundance of C-14 is less than 1 part in a trillion and the energy released by its decay is a thousandth the energy of a Uranium-235 fission. In contrast, U-235 occurs with an abundance of nearly 1%, making it profitable to extract and separate.

As a final point, we can control the rate of fission in Uranium with control rods which moderate the free neutrons. The beta decay of C-14 is probabilistic, so we get a fixed power output (which exponentially decays) which we can calculate! A C-14 decay releases 0.15 MeV of energy with 50% probability in 5700 years. This gives an C-14 atom a power output of

(0.5) × (0.15 MeV/7500 years) = 5 × 10-26 Watts/atom

In 1 kg of pure C-14 there are 4 × 10-25 atoms, so its power output is at most 2 Watts/kg! It’s barely enough to power an LED, let alone boil water and run a turbine!

 

 


 

 

asked by asked by Muskaan M

image credit: Wikimedia Commons

 


 

 

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