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I recognize the visible wavelengths of light extend from approximately 400 - 700 nm. But how many different wavelengths exist in that range? 300 ? 30,000 ? (400.01 - 699.99)

If it's completely continuous, then how can photons be so easily absorbed, as they need to match an electron potential fairly precisely to be absorbed?

(I did a naive calculation some time ago, and came up with a wavelength about every 1.5 nm, but I don't know if that is correct.)

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    $\begingroup$ You are assuming that photons are only absorbed by kicking an electron to a higher energy level. But they can be absorbed by many other processes too. $\endgroup$ – Jim Feb 18 '15 at 15:44
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spectrum of sun

As you can see the spectrum at the top of the atmosphere is continuous, with some saw tooth excesses, but still continuous.

The absorption does create a saw tooth pattern, even so there is continuity.

To dispel doubts here is the sun spectrum showing continuity and absorption spectra

absorptions spectrum

Solar spectrum with Fraunhofer lines as it appears visually.

The first figure has been done registering intensities at each wavelength.

You ask:

how can photons be so easily absorbed, as they need to match an electron potential fairly precisely to be absorbed

Photons are absorbed when they impinge on atoms with matching energies, and the others are not. Absorption is not the only interaction that photons can have. They can scatter off electrons and lose some energy, Compton Scattering, or whole atoms Raman scattering . These do not have precise energy levels.

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    $\begingroup$ I believe the sun spectrum is not related to the question. The question was probably about a potential "discrete" character of the wavelength itself, meaning that there could be forbidden and allowed wavelengths, maybe regularly spaced. $\endgroup$ – fffred Feb 18 '15 at 15:05
  • $\begingroup$ @fffred The spectrum is the experimental evidence that it is continuous. $\endgroup$ – anna v Feb 18 '15 at 15:19
  • $\begingroup$ I don't see how a chart indicates the spectrum is continuous, though that might be so. $\endgroup$ – Jiminion Feb 18 '15 at 15:19
  • $\begingroup$ I agree with @Jiminion. The spectrum data is discrete anyway, because of the limited resolution of the detector. There might be a fundamental limit to the resolution of wavelengths, or not, but we cannot infer that from the presented data. $\endgroup$ – fffred Feb 18 '15 at 15:27
  • $\begingroup$ @fffred please see my edit $\endgroup$ – anna v Feb 18 '15 at 15:41
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To my knowledge, there is no discretization of the light wavelength (they form a continuous spectrum).

On the other hand, there exists no infinitely narrow absorption "potential". I mean that all transitions of electrons that may correspond to a photon absorption have a finite width. Consequently, the photons have a non-zero probability to get absorbed.

Moreover, many materials do not have narrow energy transitions. For example, metals have free electrons (not bound to an atom, i.e. not subject to atomic transitions) that may absorb many different photon energies. Other materials absorb light through other processes, such as changes in the vibrations of molecules, or in their rotations, etc. These processes show similar transitions to atomic transitions, but these may have much wider wavelength acceptance.

(Another thing to consider: photons do not have a precisely defined wavelength due to Heisenberg uncertainty principle)

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