let me copy my little assignment note here
These are some of the uses of particle accelerator:
1. To investigate the nuclear force and the nature of the fundamental particles, the nucleus needs to be disrupted. To do this energy must be put into the nucleus.
2. The resolution that we can achieve in imaging the structure of the nucleus also depends on the de Broglie wavelength of the particle we use to probe the nucleus. The higher the particle energy, the shorter the wavelength ( = h/mv) allows more detailed structure to be observed.
3. The higher the particle energy, allows particles to come closer to each other before being deflected. Thus the smaller details of their structure can be observed by determining how they bounce off each other.
4. High energy means high mass particles can be produce (E = mc2). The vast majority of elementary particle (e.g. heavier types of quarks) can only be observed after their creation in high-energy accelerators because they are unstable and last for such a short time that there are none around us in ordinary matter.