Explain xkcd: It's 'cause you're dumb.
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I have done a bunch of things! I wrote most of explanation for 2527, and created (Badly) the page for 2616. I think I screwed that last one up though. I will add more later.

Hello people! You are probably looking for how I calculated the yield of a baloon made of helium-2 for 2649: Physics Cost-Saving Tips. Well you're in luck!

Calculation time! (Sorry). Helium-2 has a half-life of roughly 10-9 seconds, or one nanosecond, and a mean life of roughly 1.44 nanoseconds. For context, light travels at roughly 30 cm per nanosecond. This means that on a human scale the energy is released all at once, and we only have to calculate total energy released, and not worry about time taken.

Helium-2 decays through 99.99% proton emission. For simplicity's sake, we'll call that 100%. Helium-2 is formed from two hydrogen-1s, and 1.25 megaelectron-volts, or as an equation,

H +
H + 1.25 MeV =
He. It therefore follows that decay from a helium-2 atom to two hydrogen-1 atoms would release 1.25 MeV,[citation needed] per the conservation laws of energy and mass.

A moderately-sized balloon might have a diameter of 12 inches. Some calculations give this a volume of roughly 14.83 liters (assuming a spherical balloon.) If the balloon is at 1 atmosphere of pressure at 25 degrees Celsius, then there would be 0.6058 mol in the balloon, mean that there is 0.6058 * 6.022×1023 atoms, or 364,800,000,000,000,000,000,000 atoms.

To recap, a helium-2 atom decaying results in 1.25 MeV of energy, and there are roughly 365 sextillion atoms in a balloon.

Every atom will create 1.25 MeV of energy, and therefore 365 sextillion atoms will create 365*1.25 sextillion, or 456 sextillion MeV. Interestingly, this is equal to 456 nonillion electron volts, or 4.56 megayottaelectron-volts. 456 sextillion megaelectron-volts is also equal to roughly 73,100 megajoules, or 17.4 tons of TNT equivalent.

This is rather big. but not massively so. The smallest nuclear bomb, the W54, had a yield of between 10 and 1000 tons of TNT. The largest conventional bomb, the GBU-43/B MOAB, has a yield of roughly 11 tons. The M67 grenade uses 180 grams of TNT-RDX mixture. So while the Helium-2 baloon bomb would be larger than all conventional bombs, it would still be smaller than most nukes.

I have a discussion page now!