# B Recklessness with E=MC^2

1. Nov 26, 2016

### Algr

Okay, I know I have no business playing around with relativity, but things got heated and I grabbed this:

And turned it into:

Give it to me straight. Did I blow up the Earth?

2. Nov 26, 2016

### OmCheeto

Everything looks ok to me.
Released all at once, it's only equivalent to about 21 megatons of tnt.
I believe we've detonated a slightly larger bomb in the past, without blowing up the Earth.

3. Nov 26, 2016

### Staff: Mentor

2.8 billion watts is a typical total power output of nuclear and coal power plants (a bit less than half of that as electricity, the rest as heat).

The largest explosion was the Tsar bomba, about 50 megatons TNT equivalent.

4. Nov 26, 2016

### Janus

Staff Emeritus
To put this in perspective, to "blow up the Earth" (Death Star style) would require 2.24e32 joules or ~2.5e15 times the energy equivalent of that 1 kg, or what you'd get from converting 2.3 times the mass of the Martian moon Deimos into energy.

5. Nov 26, 2016

### Algr

Oh, I get it.

Uranium absorbs a neutron and becomes 236U

Then it splits into 92KR and 141BA. But 92+141=233, not 236

The missing three are the three neutrons. So Tzar Bomba is about 2.5 kilo of neutrons turned into energy?

6. Nov 26, 2016

### Staff: Mentor

Right, but you don't see that the mass reduced if you just look at the number of nucleons (that number is conserved). The neutrons are still around.
No. 2.5 kg of its original mass. It doesn't make sense to associate this to a particular decay product.

7. Nov 26, 2016

### Algr

So it weighs less, but the number of particles is the same? Do particles have variable weight?

8. Nov 26, 2016

### houlahound

Indeed, weight is position dependent.

9. Nov 26, 2016

### OmCheeto

Yes.
Only when mixed together[edit: sometimes[second edit: actually, always]], to make an atom.

see: mass per nucleon graph.

I'm not very good with words, so a graph is the only way I can understand this phenomena.

Last edited: Nov 26, 2016
10. Nov 26, 2016

### Staff: Mentor

No. The mass of N particles together is not necessarily the sum of masses of those N particles. Combine a proton and an electron to make a hydrogen atom, and a tiny bit of energy is released and the hydrogen atom is a bit lighter than "proton mass + electron mass".

For nuclear reactions the difference is more pronounced but the idea is the same.

11. Nov 26, 2016

### Staff: Mentor

The "missing" neutrons are being absorbed by other U-235 nuclei and turning them into U-236 to keep the process going - that's what makes it a chain reaction.

12. Nov 27, 2016

### Algr

But eventually you run out of uranium and still have neutrons running around everywhere. Then what? Do they make heavy isotopes of any atom they can find? Decay into hydrogen and a neutrino?

13. Nov 28, 2016

### Staff: Mentor

Nearly all are captured by other atoms in microseconds, making some of them radioactive and contributing to fallout. A few will decay, but that contribution is completely irrelevant.

14. Dec 5, 2016

### Algr

Hmmm...

We still have 2.5 kilos of "matter" in tzar bomba that isn't actually made of anything. Wierd.

Either that or E=mc^2 doesn't actually happen in a nuclear bomb at all.

15. Dec 6, 2016

### Staff: Mentor

Well, total mass is not the sum of masses of its constituents. That might appear weird, but that's how the universe is.

16. Dec 6, 2016

### Algr

I think I get it, but it seems odd to call it "matter" when it is actually the energy needed to shove particles into a difficult atom. It's more like 2.5 kilograms of energy was released.