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

**Posted on:**April 30, 2016 /

**Categories: Uncategorized**

**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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