In Planck's quantum theory of radiation we get to know light travels not continuously but discontinuously in the form of small packets of energy called quantum..... Does it means in short means that light dosnt travels in form of a wave but as a particle as if it would have traveled as a wave it would be continuous?
The classical mode leads to the ultraviolet catatstrophy, because all possible frequencies have equal probability of being occupied by radiation.
The quantized modes repress the higher frequencies, which is what is observed experimentaly.
The formula used
leads to the conclusion that each frequency comes in packets with energy = h*nu
There is a continuum of frequencies, but less occupied as the frequencies go up, in the cavity model used.
It is the photoelectric effect that identified the photon particle with energy=h*nu , and the spectra of the atoms.
Present quantum field theory explains classical electromagnetic radiation as emergent from zillions of photons, as can be seen here.
we get to know light travels not continuously but discontinuously in the form of small packets of energy called quantum
This is a common "explanation", but a confusing one.
Essentially, under quantum models, everything is "particle like". That includes light, electrons, and you. Additionally, everything is "wave like" too. We simply didn't notice this because for most large objects, like you, the wave part of its nature is not obvious.
Does it means in short means that light dosnt travels in form of a wave but as a particle
Exactly. Sort of.
Now you say, "well, ok, big deal". But this statement is a big deal. That's because we can clearly see wave-like behaviour - color is frequency for example, and that's something we've been seeing for a while now. Other optical effects, like diffraction, also suggest that "light is a wave".
Well, it turns out that electrons have a frequency too, and they diffract just like light does. It just takes a clever arrangement to see it, and we didn't figure out how to demonstrate it until 1927.
It took some time to figure all of this out. Today we see the wave-like behaviour as a side-effect of the nature of the way these "particles" behave. Or you could say these "really are" waves, but have particle-like qualities. Either is equally wrong - quanta are quanta and the "wave-like" and "particle-like" behavior are things we impose on them because we're trying to simplify our language. Light happens to look more wave like, and protons more particle like, but it's all the same under the covers.
UPDATE: It's worth nothing that it wasn't really Planck who suggested this duality, one can point to Einstein and de Broglie as the main moves in this direction. Planck saw this of something of a curious solution to a thorny problem, and I don't think he ever really enjoyed the duality that emerged.