atomic_fungus (atomic_fungus) wrote,

#4383: I have to wonder how cold the room would get, though.

The other day, during some downtime at work, I had a thought about a balloon full of helium suddenly turning into lead, and how big the piece of lead would be.

So I looked up the densities of helium and lead and worked it out.

Now, if you assume that the components of the helium atoms just suddenly rearrange themselves so that they're lead atoms, and further that the energy budget is irrelevant, then a cubic meter of helium will turn into a sphere of lead about three centimeters across. This lump of lead weighs 116.4 grams, the same as the cubic meter of helium (at one atmosphere, 20° C).

Of course that's not the whole story, because that assumes a magical process where the protons, neutrons, and electrons just magically rearrange themselves. What happens if we pay attention to the energy now?

Fusion of atoms releases energy until you get to iron. From hydrogen to manganese, fusion is a net producer of energy; once the atoms have fused and things have settled down, you have a heavier element and some excess energy. So to get from helium to manganese you've released quite a bit of energy, making the immediate environment quite toasty, and of course you don't have 116.4 grams of manganese because some of that mass got turned into energy.

But from iron onward, fusion requires an input of energy, and we have quite a way to go to get to lead (element 82) from iron (element 26). If we assume we can use the energy we had previously emitted to help out with the fusion reactions, even then we still don't end up with 116.4 grams of lead because now we're using up mass to power the fusion reactions. If you don't, you're sucking energy from the surrounding environment, and in that case I imagine the room would get chilly. I just wonder how chilly it would get.

I was satisfied with the 3 cm ball of lead answer, though. The rest of it was just fiddling. Of course, it's all about the binding energy; iron fusion (for example) is a net consumer of energy because the larger the atom's nucleus gets, the more binding energy (strong force) is required to hold the thing together, and the energy that's released from fusing the nuclei is insufficient to provide all the binding energy required for the new nucleus. Further, when a uranium atom fissions, the energy that comes out is largely that binding energy being released via one mechanism or another.

...which is why fission is "downhill", by the way. An unstable nucleus is trying to find a more stable state--a state with lower potential energy--and that's like a rock rolling down a hill. (Almost literally, as it turns out.)

And so my idle curiosity about how big a certain volume of helium would be if converted to lead somehow taught me a little bit about how and why fusion and fission behave the way they do. Whee!

(Afterthought: fission doesn't have the same sort of limit that fusion does. Tritium is a radioactive isotope of hydrogen--one proton, two neutrons--that has a half-life of about seven years. It's much easier for the rock to spontaneously roll downhill.)

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