A question about the light spectrum

[sangho]

For any given number(length), say L, is always there an electromagnetic wave with the wavelength L ?

As I know, the source of electromagnetic wave is the energy emission of electrons changing it's quantum state in an atom.
But there are at most about 120 atoms there, and the quantum numbers are, mathematically saying, countable. So I think the electromagnetic spectrum is not filled with all numbers in the axis.

 

[phyzguy]

The E-M spectrum is a continuous spectrum, and all wavelengths are possible. There are many reasons why. In the case of emission of radiation by an excited atom, since the emission of the radiation must conserve energy and momentum, the wavelength of the light emitted depends on the state of motion of the atom. Also, after a photon is emitted from an atom, the photon can scatter off of something, like a free electron, which changes its wavelength. There are also many other sources of EM radiation besides the de-excitation of an excited atom. For example, an electron scattering off a nucleus can emit radiation through bremsstrahlung. Since the electron and nucleus can have any state of motion and meet at any angle, this results in a continuous spectrum.

 

[jbriggs444]

At the very high end of the spectrum, there may not be enough energy to feasibly create an EM wave of the requisite wavelength or to survive its detection.. Though, if one is given freedom to choose one's frame of reference, then a particular EM wave can have any wavelength one chooses.

At the very low end of the spectrum, the wave may be longer than is feasible to create, detect or measure.

 

[Drakkith]

There's also the issue of doppler shift and cosmological redshift, which are both continuous in nature.