Nadia

It is worth saying that proton transfer between nuclei does happen — it is simply not chemistry.

It occurs in stars, where temperatures and pressures provide the required energy and nuclei fuse. It occurs in particle accelerators, where we supply the energy deliberately. It occurs in certain kinds of radioactive decay, where a nucleus rearranges and its proton count changes, turning one element into another.

That last one is the historical punchline: transmutation of elements, which alchemists pursued for centuries and could never achieve, is real. It just requires nuclear rather than chemical processes, and the energies involved are why no arrangement of furnaces and reagents was ever going to work.

So the honest answer to your question is that it is not impossible, it is simply not available at the energies that everyday matter operates at.

The crucial variable is temperature, expressed relative to the material's melting point rather than in absolute terms.

Creep becomes significant somewhere above roughly a third to a half of the melting temperature. For steel that is well above anything at room temperature, so a steel bar at ordinary conditions creeps immeasurably slowly. For lead, whose melting point is low, room temperature is already a substantial fraction of it — which is why old lead pipes and lead sheet on roofs visibly sag and thicken at the bottom over decades. Lead creeps at room temperature and steel effectively does not.

So the answer to "is there a threshold" is: at a given temperature there is a stress below which the rate becomes so small that other failure mechanisms will get there first, by an enormous margin. Not a true threshold, but one for practical purposes.

Worth planning the trip so descending is easy. On a drive-up mountain that is straightforward — the car is at the top — but check the return timing.

The common failure is being three hours' walk from the road at the point where somebody starts feeling bad, at which stage descending is a decision with a real cost. Keeping the first day's route short and reversible removes that entirely and costs nothing but a slightly less ambitious day.

Your reasoning is correct. It is possible, and the probability is small in a way that is genuinely difficult to convey.

Each nucleus decays independently, with a fixed probability per unit time. For a five-year half-life, the chance that a given nucleus decays in any particular minute is roughly one in two million. The chance that all of them do is that number multiplied by itself once for every nucleus present.

A kilogram of material contains something on the order of a billion billion billion nuclei. So the probability is a number like one in two million, raised to a power with twenty-something digits in the exponent.

Written out, that probability has more zeros after the decimal point than there are atoms in the observable universe. It is not merely astronomically small; it is small on a scale where the word astronomical is far too weak.

That is the part that dominates: very small black holes are predicted to evaporate, and the smaller they are, the faster and more violently.

The theoretical result is that a black hole radiates, and its temperature is inversely related to its mass. A stellar black hole is colder than empty space and grows rather than shrinks. A black hole with the mass of an apple would be extraordinarily hot and would radiate its entire mass away in a very short time.

And the mass of an apple, converted entirely to energy, is an enormous amount of energy. Released rapidly, in your kitchen, it would not be a local event — the calculation puts it well beyond anything survivable for the surrounding area.

So the answer to "would touching it kill you" is that the question does not arise, because you would not have time to reach out.