# C14 Nuclear Diamond to AA Battery Apples-to-Apples Engery output

I was reading an article about nuclear diamonds and they made an apples-to-oranges comparison of a 1 gram C14 nuclear diamond to a single AA battery. Here is the part I'm referencing:

"An alkaline AA battery weighs about 20 grams, has an energy density storage rating of 700 Joules/gram, and [uses] up this energy if operated continuously for about 24 hours." Meanwhile, "A diamond beta-battery containing 1 gram of C14 will deliver 15 Joules per day, and will continue to produce this level of output for 5,730 years — so its total energy storage rating is 2.7 TeraJ."

I'm far from a chemist or any other applicable type of scientist otherwise I'd take a crack at the answer myself. The question simply is this: according to the data provided how many Joules per gram would a C14 nuclear diamond produce if it weighed 20 grams (to compare it to the quoted AA battery that weighs 20 grams)?

To visualize the desired apples-to-apples answer:

Conventional 20 gram battery: 700 Joules/gram, for 24 hours.

Nuclear ?? gram battery: ??? Joules/gram, for 5,730 years.

• Note that the period of 5730 years corresponds to the half-life of C-14. – Loong Feb 13 '17 at 18:57
• I'll point out that the battery output was normalized to 1 gram whereas the battery was noted as weighing 20 grams. – MaxW Feb 13 '17 at 19:05
• And of course the output will be decreasing over time (implicit in the half-life, but perhaps better made explicitly). And this ignores the problem of converting the beta in to useful electrical output. Much less finding a gram of C14 (or 20g for that matter!). – Jon Custer Feb 13 '17 at 20:50

"[...] how many Joules per gram would a C14 nuclear diamond produce if it weighed 20 grams"

I think it's important to understand that the bolded/italicized phrase is redundant, because your are discussing (as did the article) the energy output per gram. So the per-gram output of a 20 gram battery is the same as that of a 1 gram battery. The 20 gram battery would have a total output of 14000 Joules in it's lifetime, where the one gram battery would have a total output of 700 Joules. The fact that the article, and your question, normalize to a per-gram basis is how they've maintained an apples-to-apples comparison.

The semantics get tricky when they talk about the mass of the diamond battery, and by my thinking this is where they may fail to give an apples-to-apples comparison. The diamond would not be pure $\ce{C^{14}}$, and at a minimum would contain a thin protective coating of non-radioactive $\ce{C^{12}}$ (protecting those on the outside from the radiation on the inside). So when they say "A diamond beta-battery containing 1 gram of $\ce{C^{14}}$", it is not made clear what the total mass of diamond would be (e.g. we aren't given the ratio of $\ce{C^{14}}$ to the $\ce{C^{12}}$ that would also be present).

That said, I think that the apples-to apples answer to your question, based on the information given in the article, is as follows:

Conventional 20 gram battery: 14000 Joules/day, for 1 day.
Nuclear 20 gram $\ce{C^{14}}$ battery: 300 Joules/day, for 5,730 years.

or, equivalently:

Conventional 1 gram battery: 700 Joules/day, for 1 day.
Nuclear 1 gram $\ce{C^{14}}$ battery: 15 Joules/day, for 5,730 years.

• I'm well aware of what half-life is as well as the fact that not all of the material is radioactive. It was more of the 15 versus 700 Joules of energy I was interested in. I suppose a secondary question would be, how large would those nuclear diamonds be in comparison? I imagine large enough to negate the size/energy efficiency of conventional batteries though the nuclear batteries certainly have a much longer shelf-life. Thank you. – John Feb 14 '17 at 9:19
• I'm glad I was able to help. Thanks for the very interesting question! – airhuff Feb 14 '17 at 10:43