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Why are available frequency of light continuous ? I keep hearing that atoms absorb (and emit ) photons of particular frequency which correspond to their energy levels of their electron. Where do all other colours come from ?

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The Doppler effect and the expansion of space are two things that are responsible for changing wavelengths. –  jhobbie Jun 25 '14 at 15:23
@jhobbie I understand what you are talking but how to link it by giving logical proof –  Murtuza Vadharia Jun 25 '14 at 15:26
@jhobbie: And maybe more importantly, the black body radiation is continuous. –  rodrigo Jun 25 '14 at 15:27
What do you mean? –  jhobbie Jun 25 '14 at 15:27
@JavierBadia: Spectral lines are so because electrons inside atoms have quantized energy levels, but thermal radiation (that of a black body) is caused by kinetic interations between atoms, and that energies are not so quantized. Hence, the thermal spectrum is very smooth, save the occasional emission or absorption line. –  rodrigo Jun 25 '14 at 15:36

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I think I see two questions in your post.

Each frequency of light will produce a color response in the brain. However, the brain is capable of perceiving colors that do not correspond to pure frequencies, for example pink, cyan, and brown. These are produced by combinations of frequencies which the brain boils down to a single color.

The statement that atoms absorb and emit single frequencies is only approximately true. If you could completely isolate an atom from any other interaction, and be made to be stationary (and isolation can very nearly be accomplished experimentally) it absorbs and emits light at very nearly a single frequency. In fact, even an ideally isolated and stationary atom will absorb and emit light in a range of frequencies, although that range is very very small for the isolated atom.

But atoms are rarely isolated. They find themselves in environments with lots of neighboring atoms. In a solid there are atoms nearby which distort the energy levels of the isolated atom, causing the frequencies of absorption and emission to broaden enormously. In a gas, atoms are not stationary, causing Doppler shifts as @jhobbie mentioned. Furthermore, they are constantly colliding with other atoms, which also leads to distortions and broadening of frequencies. In effect, in such cases, we have a situation where each individual atom finds itself in its own particular environment, and can absorb and emit at it's own peculiar frequency ... and there is an enormous range of such environments, so there can be an enormous range of frequencies.

Additionally, most materials when heated emit a continuous spectrum of frequencies due to the random collisions and vibrations of their atoms and electrons. The incandescent light bulb is a perfect example of that. It emits light at all visible frequencies.

There are several mechanisms that lead to random shifting and broadening of spectral "lines", so that in practice, all frequencies are available to form colors.

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Is the photon emission of heated objects happening via a different mechanism than the quantized electron-level jumping that causes discrete emission lines, or is the heating just broadening the effect of the kinetic energy and Doppler shifts? –  Russell Borogove Jun 25 '14 at 21:22
Mechanism is much the same. As you heat things up there's more and more kinetic energy around which can be transferred to electronic (and vibrational) levels of the molecules. The lines are additionally broadened by Doppler shifts at higher speeds. But the visible light comes from transition between states. Diamond has no states, vibrational nor electronic, that emit in the visible, so at temperatures that make tungsten glow white, diamond remains dark and transparent. –  garyp Jun 25 '14 at 22:10

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