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If the Large Hadron Collider was to produce black holes that fell to the center of the Earth, how long would we have before these black holes consumed the Earth? A good way to get a general idea of how long it would take these black holes to consume the Earth is to see how long they would take them consume a smaller amount of matter, and compare that to the total mass of the Earth.
If a micro black hole is produced at the LHC and not contained, it will fall into the earth and oscillate through it indefinitely sucking up particles as it goes. However, on the atomic level, even matter itself is mostly empty space. So as the micro black hole travels to the Earth, the amount of atoms it runs into and consumes may actually be quite small.
The Earth's density is similar to that of iron, so we will assume a micro black holes travelling through the Earth will only consume iron atoms. These atoms, on average, are evenly spaced from each other. Assuming the micro black hole's size is the same as an iron atom nucleus (when it reality it would actually be much smaller), the micro black hole would run into, and consume an iron atom every 6.7 centimeters, or every 2.6 inches. This means through one pass through the Earth, the micro black hole would consume over 94 million iron atoms! While this may sound like a lot, this is actually a very little amount of matter when you add up all the weight of the iron atoms consumed. At that rate of consumption, the black hole would have to oscillate through the Earth about 56000 billion times just to consume 1 one measly gram of matter! And it would take it about 4 billion years to do so. Based off the assumptions made above, this is actually a huge underestimate, and in reality a micro black hole would take much longer to consume a single gram of matter.
Another way to make an estimate of time until full consumption of the Earth is to use the micro black hole's Schwartzshield Radius as the effective area of collision into an iron atom. Before an assumption was made that the micro black hole would be the same size as an iron atom, where as now we are using the actual theoretical micro black hole size. The size of the micro black hole is found by assuming that all 14TeV of energy from each particle collision that will occur at the LHC would be converted into the mass of a micro black hole. The amount of time increased from 4 billion years, to a number on the order of magnitude 79 - that is a number greater than 1 followed by 79 zeros! And all just for one single gram of matter.