Continuous vs. Discrete Spectra in various materials I read that the reason solids emit continuous spectra is that they don't have time to let their electrons decay-they are too close together. Given that electrons decay on the order of 100 nanoseconds I find this difficult to believe. Also, do electromagnetic waves move the electrons, or the atom, or both? If it is simply exciting the electrons, I don't know why is should also give way to the vibration of the atoms. If it does give way to vibration, then shouldn't gases also give way to continuous spectra?
 A: These statements show great confusion in the concepts of modern physics.

I read that the reason solids emit continuous spectra is that they don't have time to let their electrons decay-they are too close together.

It is confusing to be talking of time with respect to emissions and you give no link.
To start with at the atomic level, in any phase of matter, gas,liquid,solid,plasma , the framework is quantum mechanics. Quantum mechanics works with potentials of the electrons in the atom, and between atoms/molecules and with the intermolecular van der Waals forces in the lattice of solids.
Gas atomic spectra come from excitations of the electrons and possible vibrational transitions of the atoms as they move in the gas scattering off each other. Note the high excitation values needed from the power source, 5000 volts.
High excitation values are needed to see emission spectra from solids too, but long before the input energy reaches the atomic level energies needed to excite the electronic atomic orbits the intermolecular energy lines become excited. Iron in the forge glows, mostly in the infrared. The radiation appears continuous to the eye and the instruments because there are very many energy levels between molecules overlapping in value due to the complexity of the ~10^23 molecules per mole in matter, all compressed in " touch" densely with neighbors. It is effectively the black body radiation that dominates from solids. This shows the quantum nature not in individual lines but in the avoidance of the ultraviolet catastrophe, where the model is of harmonic oscillators changing energy levels.

Given that electrons decay on the order of 100 nanoseconds

Electrons do not decay. Decay can be attributed to the de-excitation of the atom by emission or the de-excitation of the lattice in solids .
The time of de-excitation depends on the energy and conforms with the heisenberg uncertainty principle bounds. 

Also, do electromagnetic waves move the electrons, or the atom, or both? 

Both. When the frequency is right for the energy level an electron can be kicked up, or a molecule go to a higher rotational level, or an ensemble of molecules go to a higher level.

If it is simply exciting the electrons, I don't know why is should also give way to the vibration of the atoms. 

see above

If it does give way to vibration, then shouldn't gases also give way to continuous spectra?

If gases are molecular, they have molecular vibrational levels, but the frequencies will not be optical as these levels are of much softer energy. Matter in the gas phase is very diffuse and inter molecular forces exist transiently, when they scatter and transfer kinetic energy to molecular levels which then decay to ground state.
The appearance of continuum to the eye can be obtained as with mercury vapor  lamps.
 The lines are discrete.
A: Well ordinary atomic line spectra have a frequency cutoff at which point the electron is ejected from the atom.
So conversely an ionized atom, such as a free proton, can capture a free electron, which can have absolutely any energy value whatsoever, so above the atomic line spectral frequency limit, there is a true continuum spectrum corresponding to the spectra of ionized atoms.  The continuum, is NOT any comb of densely packed line spectra, it is a truly continuous spectrum, with any wavelength or frequency beyond the atomic line spectrum limit. 
For the hydrogen spectra, the ionization potential is 13.6 Volts.   From Einstein's photoelectric equation E = h.f = 1.2398 eV um we can calculate the shortest wavelength of the neutral hydrogen spectrum as 91.12 nm in the vacuum UV.   
I use a quite modern Physics Handbook, as my primary reference for accurate numerical data on physical phenomena.  It is a handbook not a text book so it does not explain; it just cites equations and numbers.  The editors, are Walter Beneson, John W. Harris, Horst Stocker and Holger Lutz.  It is a translation from the German published originally in 2000.
Under "atomic and molecular spectra" and the hydrogen atom, on page 856 Fig 25.5 they show an energy diagram of the hydrogen spectrum, with the Lyman, Balmer, Paschen, and Brackett series; with the UV Lyman series going from the zero energy level ionization level down to the -13.595 eV ground state.   Above the zero level they show a continuum for electron initial energies > zero corresponding to free electron capture by a proton.  The four series are of course for n = 1, 2, 3, 4.   They also list a fifth "Pfund" series for N=5.   They show that the bracket series extends from 1459 nm out to about 4,000 nm , with the Lyman series going from 91.16 nm out to a bit over 120 nm for the Lyman alpha line.  The line spectra of course get increasingly dense for n and m at very large values; but they still are discrete frequencies, as described by the Bohr atom theory.   The  continuum part of the spectrum, is not discrete, as the upper energy level has any positive value.   
In Planck's Black Body spectrum analysis, he ordained (in 1900) that the emitted energy AT ANY FREQUENCY must consist of an integral number of packets (photons) each of energy h.f  but he never suggested that the emission frequencies were in any way quantized or discrete as are the lines of the Bohr atom hydrogen spectrum.   The photon energies are in no way restricted to discrete values; but at ANY frequency, the photon energy is h.f which means  that Planck's constant (h) is simply the quantity of "action" contained in one cycle of the associated wave frequency.  (in units of Joule seconds).  
Planck's quantization of the black body radiation spectrum, is no more quantized than saying that the spectrum of rocks found on earth is quantized so that rocks can be counted, but you can't have 0.35 of a rock; but you can have a rock of any size you want, without restriction.   I should add that the product E.lambda is simply h.f.lambda which is simply h.c which is the 1.2398 eV Einstein constant for the photo-electric effect.
But an ionized hydrogen atom (proton) can capture an electron having any amount of kinetic energy, which can drop into any of the hydrogen quantum states, and emit a photon of any energy greater than 13.6 eV, depending on the initial energy of the captured electron, and the result is a non-quantized continuum spectrum continuing on down from 91.12 nm to much shorter wavelengths in the gamma spectrum.  
