What does one mean by normal mode of an object? Why is it 3n-5 for linear particles, 3n-6 for non linear particle where n is the number of particle.
A normal mode is a specific type of vibration that a molecule can exhibit. They are "normal" because each type of vibration is distinct and cannot be replicated by any combination of the other types. Any possible type of vibration that a molecule can exhibit is just a combination of its normal modes. The numbers can probably be derived from symmetry arguments, I don't know how, but it's easier just to draw out molecules for n = 2 and 3 and try to convince yourself that there is an agreement with the formulas.
There are loads, Bernath (2005) is pretty good for a conceptual overview in the context of spectroscopy, should be in most scientific libraries. But if you're serious about molecular spectroscopy.... Penner or Herzberg are solid, detailed (if a little old) texts.
