I have a very normal yet a curious question about the double slit experiment. No one takes much interest in my college to explain the stuff. Instead they are all just busy to complete the syllabus so no point in asking them. At first I thought that this question is stupid but now am asking. How does the particle coming out of the particle accelerator doesn't hit the space in between the two slits? Does it diverge in a curved path before going through any one of the slit? And if it does diverge, then why?
Most particles do hit that space, and are blocked. The source of particles must be such that it emits in all directions. Often, something is done to simulate a point source. An ideal point source emits in all directions. For example, in the case of light, a single slit is put in place before the double slit. The single slit simulates a point source and radiates in all forward directions.
Update after @Jaywalker's answer
@Jaywalker brings up an important aspect that I glossed over: How to reconcile the wave picture and the particle picture? How can a single "particle" (say, an electron) be launched toward both slits? The answer depends on what we think about when we say "particle". If we mean a tiny little object that moves through space like a projectile, then the answer is "it can't". This is primary evidence that that picture of "particle" is not a good description of what is going on. In short, all "particles", including electrons and photons, are quantized excitations of a field. Energy and momentum are transferred at particular locations, giving the impression that a object hit something. The field exists everywhere in space except where space is occupied by an obstruction. The excitation of the field (the "particle") exists everywhere, but the interactions occur at particular locations. The field obeys some wave equation, and thus exhibits interference.
Really when dealing with this problem, the particle can not be considered as a particle but a wave. The wave is emitted in all directions and a small portion of it goes through the slits. Another part reflects off the wall inbetween the slits. If a source of single particles like an electron gun was pointed at the slits, indeed a portion of the total number of particles have a chance of reflecting off the barrier between the slits.
The problem here is to distinguish between theory, facts and interpretations. The facts related to the two-slit experiment is that one particle always arrives as a point. If you have enough particles in sequence, a diffraction pattern becomes discernible that is consistent with the proposition that a wave diffraction pattern gives the probability that a given particle will arrive at a given point. We also believe the experiment complies with the laws of conservation of energy and of momentum. We also know if we shine strong light on the particles as they exit the slits, the diffraction pattern disappears, and we get the pattern, more or less, of one electron having gone through one known slit.
Either there is a wave and a particle, or there is not. In the Copenhagen Interpretation, there appears to be not a wave as such, and the effect happens merely to comply with an equation, and the whole issue is left afloat. The premise that there is a wave was followed separately by de Broglie and Bohm, and this is the interpretation I follow, although I have made some alterations in that I add the requirement that the phase term follows Euler and becomes real at the antinode (and I attach physical significance to that at times) and that the phase velocity must equal the particle velocity to affect the wave. That requires the wave to transmit energy, and I assume it guides the wave through an energy field. Where the energy is is admittedly a problem, and it effectively requires another dimension, which some will regard as ugly. I call these guidance waves, to slightly differentiate them from the pilot wave.
The important point is that weak measurements (Kocsis, S. and 6 others. 2011. Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer Science 332: 1170 – 1173.) indicate that when emerging from the slit the photon follows a trajectory in accord with that predicted by Bohm, which, in my opinion, is strong evidence in support of the wave plus particle concept, and does not sit at all well with the distributed quantum field, or the probability distribution until observed concept.