How can we be sure smashing atoms in an atom smasher does not cause harm? I have a question about atom smashers in accelerators. How can scientists performing these experiments be sure that by smashing atoms they will not be producing the effect of a bomb, thus potentially harm. After all, they do not know the results of the experiments, do they?
The results, as advertised on television, always, after all, seem, to be novel, and seem to comprise breakthroughs.
Thank you for your answers.
 A: The answers given so far are greatly oversimplified. One of the theories that the LHC was designed to test was the idea that there were large extra dimensions: https://en.wikipedia.org/wiki/Large_extra_dimensions . If this theory had been correct, then the LHC would have produced microscopic black holes.
A fallacious reassurance against a bad outcome from producing these black holes is that cosmic ray reactions would have already been producing them. Actually, this is wrong, because cosmic ray reactions produce products with very large recoil velocities, so black holes produced in such reactions would have flown off harmlessly (passing through the earth in the cases where that was the direction of flight). In LHC collisions, a certain fraction of collisions result in products whose velocities are low enough that they are not moving at escape velocity from the earth.
A better argument is that based on the way quantum mechanics works, we're pretty sure that if a reaction can produce black holes with a decent cross-section, then those same black holes should also decay quite fast. But this was a little risky, because there is no direct evidence that black holes obey the laws of quantum mechanics as currently formulated, and in fact there are reasons to believe that general relativity is incompatible with our current understanding of quantum mechanics.
I can't find the reference now, but there was a long paper written on this before the LHC started up. IIRC the best and most model-independent arguments were based on the fact that white dwarfs (unlike the earth) would have been destroyed by any non-decaying black holes produced by high-energy cosmic rays. I think the reasoning was quite intricate and depended somewhat on estimates of the rate at which microscopic black holes would eat various forms of matter (I guess degenerate white dwarf matter), and these estimates in turn depended on the number of extra dimensions hypothesized.
A: To try and give a little more detail than the other answer - the energy of a single proton in an "atom smasher" like the LHC is less than the kinetic energy of a typical flying mosquito:
https://www.lhc-closer.es/taking_a_closer_look_at_lhc/0.energy
Of course, the trick is that the energy of the mosquito is distributed amoung it's $\sim 10^{23}$ other molecules, instead of focused on a single atom, like in the LHC.
In addition, the interactions that are going on during the collision are not the same kind of reactions that are going on in something like a nuclear weapon. In those weapons, some kind of cascade effect is required - roughly, each atomic decay produces more decays, so the effect is explosive. This is facilitated by relatively high density material (so there are more nuclei around to decay). That's the opposite thing that goes in the LHC, in which the density is very low - like 1 or several proton-proton interactions at a time.
There are in fact hypothetical dangers from these high-energy experiments. For example, since they do create high energy density situations, in principle things like Black Holes could form. However, since the energy is still relatively small, these black holes would be microscopic and pose no danger to the experimenters or the world:
https://angelsanddemons.web.cern.ch/faq/black-hole.html
Actually, it would be an incredible scientific achievement if we could produce such a quantum black hole!
A: In addition to the other points, I would add that nature is a far more powerful particle accelerator than anything we can manage. The most energetic cosmic rays ever observed have had an energy over a million times larger than the maximum reached at the LHC. Particles with these level of energy are rare, but given that we have seen several of them over the limited time and space that we have been able to track, it is a safe bet that the Earth has been hit by many over the course of human history, we would know if they were causing anything dramatic on a macro scale.
For more information, see this nice summary by CERN themselves.
Edit: Hritik Narayan posted at the same time I was writing this with a similar answer.
A: The energies of the interactions of cosmic rays from outer space in the upper layers of the atmosphere are sometimes many orders of magnitude higher than those achieved in the LHC. So if something untoward could happen from such experiments, it already would have in the sky.
The LHC operates at $\mathrm{13}$ $\mathrm{TeV}$ which is close to $2*10^{-6}$ $\mathrm{Joules}$, whereas the highest energy cosmic ray observed, the Oh-My-God particle had an energy of roughly $51$ $\mathrm{Joules}$.
A: The energies involved in "smashing" atoms is larger for an atom , but nothing compared with the energy of a ordinary bomb. Do zur Energie released by one fast atom is less than what you would need to heat 1mg of water 1°K.
The only possible damage is for people staying to close to the smashing, but nobody is allowed in the dangerous region
A: 
...the effect of a bomb...

Are you talking about radioactive fallout?
A high-energy particle accelerator does, in fact, create some radioactivity;* but unlike a nuclear weapon, the accelerator does not explode and release the radioactivity into the environment.
Most of the radioactivity in an accelerator is immobile, trapped in the solid material comprising the accelerator and its supporting structures. Also, I have reason to believe that it is mostly short-lived—that it is safe for personnel to work near the accelerator within minutes or hours of switching it off.

* https://journals.aps.org/prab/pdf/10.1103/PhysRevSTAB.17.084701
