I still don't get what it means for atomic energy levels to be continuous or quantitized (incontinuous). Clearing this up will really help me. Also, can anyone tell me why energy levels in solids are continuous while in gases they are quantitized? I get the part about the energy bands being more clustered due to the close proximity that the atoms in solids are, while in gases they are farther apart, but I don't get how this affects the absorption/released ray spectrums and how even THIS affects whether it is continuous or quantitized.
[Physics] Quantization vs. continuous energy levels
atomic-physicsdiscreteelectronic-band-theoryenergyquantum mechanics
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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.
In liquids and solids the difference in energy between energy levels becomes very small, due to the electron clouds of several atoms bein in very close proximity of one another. These similar energy levels will form 'bands' of indistinguishable spectral lines.
In gases however, atoms will be spaced loosely enough such that the interaction between atoms will be minimal. This allows the energy levels to have sufficient difference in energy for distinct lines to be formed.
Best Answer
The quantization of energy levels appears both in quantum and classical mechanics, and it is not a consequence of the Schrödinger equation. It is a consequence of confinement. In fact, anytime that a wave equation (any quantum equation for the wavefunction, or a classical equation for a classical field, e.g., EM field) has periodic boundary conditions in some spatial variables, the system exhibits quantized energy levels.
As noticed in the question and in other answers, energy levels in quantum systems are not always quantized. On the other hand, also classical systems exhibits quantization of the energy levels. For example, consider the allowed frequencies of a string with fixed length (confinement), as in a guitar or violin. In such a string, the allowed "energy states" corresponds to frequencies (harmonics) which are multiples of a fundamental frequency (first harmonic).
In the quantum realm, energy levels are quantized if the wavefunction is confined in a finite space, e.g., in an atomic orbital or in a quantum well. In a solid, energy levels are also quantized, but the difference $\Delta$ between levels decreases as the system size increases. Therefore in the thermodynamical limit (large system sizes), these quantized energy levels become a continuum of states, since $\Delta\rightarrow0$.
As an example, let us consider a plane wave $$\psi(r)\propto e^{\imath k r},$$ which describes the wavefunction of a free particle (or the propagation of a sinusoidal wave of a classical field). The wavefunction has a continuous of energy levels $\omega\propto k^2$. However, if one confines the wavefunction in the segment $[0,L]$ one has that $\psi(0)=\psi(L)$ which gives $e^{\imath k L}=1$, and therefore the only wavenumber $k$ allowed are $k=2\pi n/L$. Hence, the energy levels of the confined particle are $$ \omega\propto \frac{n^2}{L^2}.$$ The gap $\Delta_n$ between energy levels goes to zero for $L\rightarrow\infty$. Therefore, if the particle is confined ($L<\infty$) the energy spectrum is quantized (finite and discrete energy levels, $\Delta_n$ is finite). If the particle is not confined ($L\rightarrow \infty$) the spectrum is continuous ($\Delta_n\rightarrow 0$). In real solids, $L$ is typically huge with respect to the typical sizes of the ion lattice, and therefore one is in the limit $L\rightarrow\infty$.