Does the Large Hadron Collider have the potential to destroy Earth? Yes. Will it? No, but there is a long shot. What the Hadron smasher will do is smash two “things” together so that they form a singularity, a black hole. Once the black hole is created all the time and space around it will be vastly different from the time and space we have here on Earth.
Time and space is a by product of mass, which when all pulled together creates gravity. The space/time around a black is not understood. It could be an infinity slower than our time, or there could be no time at all, just sort of a nothingness going nowhere. It is the property of time warping that gives the black hole its enormous potential. Potential is the possibility of a future occurrence, in our time. What potential means to a black hole is any ones guess. But the warping of space around a black hole can cause huge changes in the environment that envelopes it. Most of the black holes out in space got their start in a super nova explosion, but there are some that have been created by other interactions with their environment. It is those type of black holes that represent the potential of the black hole that the LHC might create.
Once the black hole is created there is no going back. Size is a factor of time and space, so the size of the black hole is judged differently that the size of an atom. The black hole “size” is much larger than the “size” of the earth. The “time” it would take to transverse the circumference of the black hole, no matter what “size” it is, is infinite. This time warping is what makes a black hole a black hole. So even though the object being created is atom size, it is atom size relative to our conception of size. The black hole is infinitively large in any real earth terms. If time is considered in the description.
Will this tiny speck of infinity suck up there Earth. It is highly unlikely. Time is a relative concept, in fact time and gravity can create different dimensions, which is what a black hole is closer too than objects as we know them. Nevertheless, the timeless/space that surrounds a black hole can create disturbances in the time/space area in which it resides. These effects are poorly understood at best. A guess would be that the black hole “appears” then “disappears”, it will do this in our time and space, but in the black holes time and space it will be locked in forever, at least our forever and all the space and time around it will form a snap shot of what was going on when it formed. This snap shop has a reach that is in no way predictable from our side of the time tracks. But my best guess is we will be just fine, but there is the potential to devour all that it comes into contact with and that includes our space/time continuum.