Is Fissile Material Worth its Weight in Gold?

The other day a friend of mine made an off-handed remark to me about how nice it would be if a nuclear reactor made gold. This got me a little curious, and so I did a little research to see if gold was one of the products of fission. Well, it’s not. Gold has only a single natural isotope, gold-197, and this is substantially heavier than any of the products of fission, which have masses that range from about 75 up to about 160.

But then I had another thought: which would be a more valuable scenario?

1. A nuclear reactor that fulfilled the old alchemist’s dream of turning a metal into gold, or,

2. The way things really work today, where a fissile material (usually uranium-235) fissions and releases energy.

I mean, for just a moment, imagine a kind of nuclear reactor where uranium-235, instead of splitting, actually turned into gold. Wouldn’t we be trying to find all the cheap uranium that we could and frantically loading into this imaginary nuclear reactor so we could make gold from it?

I’m no precious metals trader, but I happened to notice that gold was trading at about $1500 per troy ounce recently. I whipped out my handy-dandy 20-year-old HP48SX calculator and put that into units that an engineer like me is a little more familiar with.

Gold has a value of about $48,000 per kilogram.

A kilogram of pure uranium-235 contains 2.56 trillion trillion (2.56 x 1024) atoms of uranium-235. When they fission, each one releases about 200 million electron-volts (200 MeV) of recoverable energy. Altogether, that’s about 82 trillion joules of energy.

In a typical light-water reactor that heat energy would be converted to electrical energy at about 1/3rd efficiency. So 82 trillion joules of heat energy would become 27 trillion joules of electricity and 55 trillion joules of waste heat energy that would be rejected to the environment.

27 trillion joules of electrical energy is the same as 7600 megawatt-hours of electrical energy.

One megawatt-hour has a wholesale cost in the US of about $40, so 7600 MW*hr would be worth about $300,000.

If we had a hypothetical nuclear reactor that could turn fissile material to gold, it would make about $50,000 for each kilogram it transmuted. But in the real world where real reactors release energy from the fission of fissile material, that’s worth $300,000 per kilogram fissioned.

That’s a six-to-one difference.

That’s pretty amazing.

I like the real world better.

(this post was originally published on Forbes)

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