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Some bulletproof safes are sturdy enough to handle grenade impacts. Could we theoretically make an analogous atomic-proof safe that will handle something like an Hydrogen Bomb? It doesn't matter the shape of it or if it has a door or handles, the materials use to build it or if it has air on the inside. As long as we can cover the whole device and prevent any significant mechanical damage to be done on the outside, I'll consider it good enough for the task.

EDIT: I'm so sorry for not being clear enough, and I've seen really great answers to this question, some of which seems to me to actually solve this problem. What I mean is: what would happen if the bomb got detonated inside this huge safe. Like, it seems clear to me that a lead safe with the size of the earth with the radius of the planet as it's thickness would be more than enough to protect someone at the surface from the blast. So, with that said, what would be the minimum necessary to muffle the explosion?

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This would depend on the location of the safe in relation to the blast. It would also depend on the yield or output energy of the blast. It also depends on whether it was detonated in the atmosphere or on the ground.

Everything would be literally vaporised at actual ground zero where the bomb was dropped or detonated, and the same for everything directly below it if it was detonated in the atmosphere. No safe, no matter how well built, will handle the temperatures.

For example, the little boy atomic bomb dropped on Hiroshima, created temperatures of $3 \times 10^5 K$. The most temperature resistant substances known to man are Tantalum and Hafnium Carbide Alloy which have melting points of $4150 K$ and $4201 K$ respectively, and their "alloy" with a composition $\text{Ta}_4 \text{Hf} \text{C}_5$ is believed to have a melting point of $4263 K$.

As you can see, these temperatures pale in comparison to that output by "Little boy". And today's nuclear weapons have significantly higher yield. This means that you could not make a safe that would protect you from such a blast, unless you are a reasonable distance away.

The further you move away from ground zero, the more likely a nuclear bomb-proof safe (or any bomb proof material) will survive.

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  • $\begingroup$ I'm chosing your answer as the accepted one since you mentioned the melting of the safe itself, which clearly would be a big problem. I'l ask you to see the edit I made to the post, but I can imagine that the safe would have to be at least large enough to prevent the heat from melting all of it and coming to the outside (kinda like how a planet has a molten radioactive core on the inside, but a safe crust on the outside). Anyway, thanks! $\endgroup$ – Evandro Teixeira Jan 10 at 3:19
  • $\begingroup$ No worries Evandro. $\endgroup$ – joseph h Jan 10 at 3:52
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It depends on how far away the bomb is, and what you consider to be a safe.

In the 1950's people built bomb shelters. It was to keep you safe if the bomb was close enough to, say, destroy your house. You could put your valuables in one and call it a safe.

It might not help if your house was at ground zero. There are scaled up plans and/or versions of the same idea. For example, see Presidential Emergency Operations Center, Deep Underground Command Center, and Cheyenne Mountain Complex

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  • $\begingroup$ Actually, I meant for the bomb to be inside the safe. Check my edit for more details, but thank you nonethless! $\endgroup$ – Evandro Teixeira Jan 10 at 3:21
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If you set the maximum explosion size a container can be made thick enough so the centre is far enough away from the outside not to be damaged by the explosion. The outside has to be able to suffer some damage. As mmesser314 said, it depends on what you would call a safe.

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  • $\begingroup$ Actually, I meant for the bomb to be inside the safe. Check my edit for more details, but thank you nonethless! $\endgroup$ – Evandro Teixeira Jan 10 at 3:20
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This is mostly an engineering concern. Thanks to $\sigma T^4$, these hot things the size of a grapefruit lose energy quickly. The actual reactions producing the majority of the energy are over in well under a microsecond. A fusion device has 50-ish nanoseconds before the fission blast destroys it.

A test was done, putting various metal spheres at different distances from a device, and have been reviewed here.

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  • $\begingroup$ Actually, I meant for the bomb to be inside the safe. Check my edit for more details, but thank you nonethless! $\endgroup$ – Evandro Teixeira Jan 10 at 3:21
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Like an underground nuclear bomb test? They design the cavern to hold the blast and all of the fission products from the blast. Most of the pressure is eventually released from the cavern due diffusion of the air through through the rocks, but it does show that it is possible.

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