Dietrich ZawischaContact German version
 

Atomic spectra

Light emitted or absorbed by single atoms contributes only very little to the colours of our surroundings. Neon signs (or other gas discharge tubes) as used for advertising, sodium or mercury vapour lamps show atomic emission; the colours of fireworks are due to it. The aurora borealis (northern light) is very rare at our latitudes, and to appreciate the colours of cosmic objects, powerful telescopes are necessary. Neon, which gives red colour in a gas discharge, is a colourless gas. If the light of the sun is spread out into different colours by a simple glass prism, the narrow absorption lines cannot be seen.





Firework. Photo © Pete Lawrence, http://www.digitalsky.org.uk/,
Shown with permission.
    

Nevertheless, to understand how the colours which surround us come about, one needs some basic knowledge on the smallest parts of matter.

Atomic structure

Only with quantum theory atomic structure can be understood. Quantum theory is, so to say, the mathematical formulation of particle–wave duality. While we cannot dive into mathematical details here, the basic principles shall be sketched.

Waves always have some spatial extension, while one may imagine the elementary, indivisible particles as being "pointlike". The fact that these apparently contradictory attributes are compatible in matter waves and also in light (photons) is hard to understand, but all experimental data point out that this is the case.

Thus the electrons bound by electric force to an atomic nucleus (which contains almost all of the atom's mass) must be considered to be waves. Wavefunctions are used to calculate observable quantities; in particular, the probability to find the (pointlike) particle in some volume is given by the squared value of the wavefunction integrated over the volume.

The hydrogen atom is the simplest of all atoms. Its nucleus carries one unit of positive elementary charge and thus binds only one electron to it. Its possible wavefunctions can be obtained as solutions of the Schrödinger equation. This is described in detail in all textbooks on quantum mechanics. For us it is important to realize that the electron forms some kind of standing wave. Some simple examples will be used to demonstrate general properties of oscillating systems, standing waves in particular.

Normal modes

The exact way how a guitar's string vibrates depends on the spot where it has been plucked. It is always possible to describe the motion of the string as a superposition of simple modes which have the peculiar property that all parts of the string move sinusoidally with the same frequency and phase. These are called normal modes or eigenmodes. The superposition of different normal modes is heard as superposition of ground- and overtones.

The picture below shows how a string vibrates in the lowest three normal modes. The motion is so fast that it cannot be resolved by the eye, one sees a sequence of nodes and antinodes.

key tone
first harmonic
second harmonic

Important properties of three-dimensional waves cannot be seen on strings; vibrating membranes show somewhat more. Instead of nodes the normal modes exhibit nodal lines. In the case of vibrating metal plates, the nodal lines are known from classroom demonstrations as Chladni figures.

Water waves are more difficult to describe than those which we are interested in. If we restrict the considerations to small amplitudes, we may neglect that. Water waves have the advantage to be slow and the wave motion can clearly be seen. The following pictures are idealized and in slow motion.

In the simplest mode in a glass of water, which can easily be excited, the liquid is swashing to and fro. This can happen in an arbitrary direction and therefore there are infinitely many standing waves of that kind, all with the same oscillation frequency.

animated picture       Double-clicking one of the images will switch on the animation; a single click switches it off again.
(a)(b) (c)(d)
An essential property of waves is that they can be added (superposed). By a linear combination (i.e. superposition) of the modes shown in figure (a) and (b) with suitable weight factors, all the infinitely many others can be obtained. Also the modes shown in Figures (c) and (d) may be obtained from a superposition of (a) and (b), with phase shifts of 90º or –90º, respectively. Therefore, there are only two linearly independent normal modes of the swashing type.
   
(e)     (f)(g)

The mode of figure (e) can be excited by falling drops. It has rotational symmetry and therefore there is no other possible orientation. The mode (f) may be obtained by gently shaking the glass with the right frequency; again different directions of motion are possible, and, similar to the above, there are two linearly independent modes, the superposition of which will yield all the others, in particular also waves going round clockwise or counterclockwise (g). The dark spot in the middle of the surface indicates that this point does not move.


Elektron clouds in the hydrogen atom

To illustrate the matter waves of the electron in an hydrogen atom, the square of the local amplitude is plotted. This quantity is identical with the particle density, and this cloudy density distribution is plotted as a white mist over a dark background. Each of the clouds shown contains exactly the one electron of the hydrogen atom, even if it consists of several distinct parts.

1s
The state with lowest energy is spherically symmetric without any nodes. The electron is very close to the nucleus.

Scale: The width of this and the following pictures is sixty times the Bohr radius, i.e. 3.17 nm.


2s

2p
For the next higher possible energy, two states of different shape are possible. One of them is spherically symmetric and has a spherical nodal area (left), the other is rotationally symmetric around a symmetry axis. The symmetry axis is vertical in the right picture, but it may have any orientation in space. Each one of these infinitely many functions may be written as a superposition (linear combination) of three basis functions, the symmetry axes of which are conveniently chosen along the coordinate axes.
The energy states are labeled by a number n which is called "principal quantum number". The number of the ground state is n=1, that of the first excited state is n=2, and so on. The letters s, p, d, f written after the principal quantum number under the images originate from properties which in early times were supposed in these states: (sharp, principal, diffuse, fundamental); these letters stand for the "azimuthal quantum number" which is the quantum number of orbital angular momentum, and s means l = 0, p means l = 1, d stands for l = 2, f for l = 3, and then it continues with the alphabet.


3s

3p

3d

Three different shapes of waves belong to the next higher possible energy. One of them is again spherically symmetric (left), the other rotationally symmetric around a symmetry axis (vertical in the picture in the middle) which may have any direction in space, and, exactly as discussed above, all orientations can be considered as linear combinations of three suitably chosen basis functions. The third kind of electron cloud for this energy exhibits two nodal planes; the centroids of the four parts lie in a plane (which is the plane of the screen in the right picture). Again, any orientation in space is possible, and again all of these may be obtained as a superposition of a few suitably chosen basis functions.

Assume that the center of force is the origin, the x-axis is perpendicular to the plane of the screen and pointing outwards, the y-axis points to the right and the z-axis upwards.

It is easy to figure out six different 3d electron clouds in special orientations in the coordinate system chosen. In the picture shown above, the maxima of the density are in the y-z-plane, and the x-y and x-z planes are nodal planes.
If the cloud is rotated by 90º around the z-axis, the maxima are located in the z-x-plane – this is the second simple special orientation, and the third one is that where the maxima are in the x-y-plane.
Next we assume the 3d-cloud of the figure above to be rotated by 45º around the x-axis. This yields the density distribution shown to the left. Here the maxima of the density lie on the coordinate axes in the y-z-plane. Two more states again result from rotations by 90º around the z- and y-axis, respectively.

Now let us take a closer look at the latter three ones. For this purpose, it is convenient to write down the wave-functions. We denote by r the distance from the origin; r2 = x2 + y2 + z2. The three functions can be written as

(y2z2) f(r),
(z2x2) f(r),  and
(x2y2) f(r).
Adding these three expressions, the sum is zero. In other words: the sixth of the functions which we have found can be written as a linear combination of the fourth and the fifth, and thus is not independent of the others.

3d (m=0)
Instead of the three functions written above one usually choses the last one and the difference of the first two lines (divided by the squareroot of 3). The corresponding density distribution is shown at the left; it is rotationally symmetric around the vertical z-axis.


Note
The selection of base functions sketched here for the hydrogen atom is different from the one presented in most textbooks. For several reasons in most cases another selection is preferrable, instead of standing waves with fixed orientation in space one chooses waves with definite projections of angular momentum onto the z-axis. Our choice corresponds to cases (a) and (b) in the above mentioned water-waves model, the latter ones to cases (c) and (d).

Energy level scheme and spectrum of hydrogen

The Schrödinger equation supplies both the energies and the wavefunctions of the possible states of an electron in a Coulomb potential well (hydrogen atom and hydrogenlike ions). The zero of the energy scale is chosen to correspond to infinite separation of an electron at rest from the nucleus. Then the energies of the bound states are negative and the absolute values are equal to the minimum energy necessary to ionize the atom i.e. to separate the electron from the nucleus.
E1 = –13.6 eV
For an electron in a Coulomb potential, the energies depend only on the principal quantum number (which we have introduced by simply numbering the energies):
En = E1/n2,
and thus the following level scheme results:

Energy level scheme of the hydrogen atom. The levels have been drawn separately for the different values of (orbital) angular momentum and are labelled by the principal quantum number n and the azimuthal quantum number, where the letters s, p, d, f, g, h stand for l = 0, 1, 2, 3, 4, 5, respectively.

Transitions from lower to higher states can occur if the necessary energy is supplied by an electromagnetic wave or by a collision with an other particle (if the temperature is high enough), and vice versa transitions from higher to lower states can occur through emission of radiation or in collisions with other atoms or molecules. The emitted photons carry the energy difference between initial and final state of the atom. For photons, the basic quantum mechanical relation between energy and frequency ν holds (h is the Planck constant):

Ephoton = h ν
This yields the wavelength   λ = c/ν   where c is the velocity of light, and finally for a transition from an initial state with number ni to a final one nf
1/λ = (1/nf2 – 1/ni2) |E1| / hc
Only the lines with nf = 2 are in the visible range (Balmer series). The result is shown below. The lines with nf = 1 (Lyman series) belong to the ultraviolet region, those with nf > 2 (Paschen, Brackett, and Pfund series) to the infrared.

Computed visible part of the hydrogen spectrum. The scale gives the wavelength in nm (nanometers). In experiment, the spectral lines are images of the spectroscope's entrance slit which occur on different places depending on the wavelength.

Starting from the Schrödinger equation we have obtained the emission spectrum of the hydrogen atom. Historically, the path towards knowledge was worked through in the opposite direction.

Some remarks on matter waves: we have used the analogy with water waves and other mechanical oscillations to make their properties plausible. But – until now nothing has been seen of any wavy motion! Indeed there really is no motion in states of fixed energy, such states are "stationary". This is due to the peculiar quantum mechanical time dependence: instead of being like cos(ωt + φ) it is described by ei (ωt + φ) (with ω = 2πν = 2πE/h). But if there is a mixture of states with different energies (and thus different frequencies), there is real time dependence. An example is given in the following slow motion pictures:



3d

Superposition of 2p and 3d

2p
Two stationary states of the hydrogen atom and a superposition of both. On "mouse over", the time dependence is shown by animation.

In times of the old Bohr Theory of Quanta, the transition from one energy eigenstate to an other one has been called "quantum leap", this notion has even found its way into colloquial language (at least in German). However, the conception of leaps is not necessary. Though it is not possible to observe such a transition in detail – it is an appealing idea that the initial state continuously changes into the final one, while the electric charge oscillates and emits (or absorbs) an electromagnetic wave.

The periodic system of elements

After hydrogen, the helium atom is the next simplest atom. Its nucleus carries two units of positive electric charge and binds two electrons. An exact analytical solution of the Schrödinger equation is no longer possible, one has to use approximate or numerical methods.

In an approximate treatment of atoms with more than one electron one replaces the interaction between electrons by a static potential. At large distance from the nucleus, an electron "feels" attraction by the nucleus and repulsion by the other electrons which screens the attraction. The closer the electron comes to the nucleus, the weaker is this screening. The effective potential for an electron in a neutral atom approaches the Coulomb potential of a single elementary charge for large distances, while for very small distances, that of the full nuclear charge.

The change of the potential affects the shape of the wave functions and the resulting density distributions (electron clouds), but the general appearance is not changed, in particular the symmetries and the ordering of nodal surfaces remain the same.


1s
Here, the density distributions of the electron in some selected modes of the hydrogen atom are shown once more; all in the same scale (the width of each picture is 3.17 nm).

2s

2p

3s

3p

3d

3d (m=0)

4s

4p

4d

4d (m=0)

4f

4f (m=0)

It is a peculiarity of the Coulomb potential that states with the same principal, but different azimuthal quantum numbers have the same energy. If the effective potential is close to that of a single elementary charge at large radii, but more attractive near the nucleus, then electrons in s-states will "feel" this most strongly, as the density has its maximum just at the nucleus. Of all the states with the same principal quantum number n, those with l = 0 are lowered in energy more than those with l = 1, these more than those with l = 2 and so on, for the larger l is, the larger is the distance of the electron clouds to the nucleus, as can be seen in the pictures above.

Now our preliminary definition of the principal quantum number as the number of the energy level is no longer true. Denoting by nr the number of spherical nodal surfaces, by l the azimuthal (orbital angular momentum) quantum number, then n can be defined as

n = nr + l + 1,

and then n and l can be used to label the states as before.

In the ground state of the helium atom, both electrons occupy the lowest possible single particle level 1s, this is denoted by 1s2.

One might expect that in the lithium atom (the nucleus of which has three units of positive charge) the electron configuration is 1s3. But this is not the case. What one has learned from the optical spectra is, that only two electrons may be in the lowest single particle state, the next one must be content with the next higher one which is the 2s state. Thus the electron configuration of Lithium is 1s22s.

The periodic system of elements can only be explained if one assumes that every single particle mode characterized by the two quantum numbers n and l and its orientation in space can only be taken on by two electrons. These two electrons must differ in an other property characterized by one more quantum number (the spin quantum number) which can only take two values, 1/2 or –1/2. This is a special case of the more general Pauli principle (Wolfgang Pauli 1924) which says that the states of two electrons (at the same place) never can be identical in all quantum numbers.

Therefore it is important to know how many independent orientations are possible for a given shape of a mode. The s-waves are spherically symmetric, thus there is only one s-wave for every principal quantum number. We have seen that a p-wave in an arbitrary direction can always be written as a superposition of three independent basis functions, thus there are three independent p-waves for each n, which can be chosen along the coordinate axes. For the d-waves (l=2), we have seen that there are five independent functions, and it generally holds that for each value of l there are 2l+1 independent possible orientations, which for free atoms usually are labelled by the magnetic quantum number ml which can take on integer values from –l to l.

Considering a nucleus with multiple charge Z and "filling in" electrons successively in the lowest possible state (as allowed by the Pauli principle), the following sequence is obtained:

1s, 2s, 2p, 3s, 3p, (4s, 3d), 4p, (5s, 4d), 5p, 6s, (4f, 5d), 6p, 7s, (5f, 6d), 7p

The levels written in brackets are very close in energy, with the consequence that, when electrons are successively added, the second level in the bracket gets some occupation already before the first one is completely filled.

As an example the electron configuration of molybdenum:

42Mo:  1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d10, 4p6, 5s1, 4d5.
The density distributions shown above illustrate that the spacial extension increases rapidly with increasing principal quantum number n. The set of states with the same n is called a shell; in real space, the different shells are not well separated from each other, but states of the same shell have roughly the same spatial extension. States with the same n and l form subshells. If all states of a subshell are occupied by electrons, their density distribution is spherically symmetric. A shell completely filled with electrons is particularly stable and therefore chemically inert. The possible interactions of an atom with its neighbours – the chemical properties – are essentially determined by the outermost electrons. From the order of levels given above and the fact that the same symmetry properties occur repeatedly, the periodic table of the elements results.

Flame test, spectroscopy

Hydrogen is a colourless gas; under "normal" circumstances the atoms are bound in pairs to H2-molecules and nothing can be seen of the possibility that light may be absorbed or emitted. Air (mainly nitrogen and oxygen) and the noble gases are colourless, and the same holds for many other substances. To observe emission of light or even spectral lines, one has to supply energy to excite the atoms.
In a gas discharge tube, the molecules are broken by collisions with electrons and ions, atoms are excited or even ionized by collisions, and then emission of light as well as absorption can be observed.

High temperatures have the same effect: in the sun there is atomic hydrogen in excited states, and in the solar spectrum the absorption lines of hydrogen can be seen.

The temperature of the flame of a Bunsen burner is sufficiently high to split molecules and to ionize atoms which after recombination give off their energy by emission of photons. With traces of alkali metal or alkaline earth metal ions (and other substances as well) flames can be coloured; this is used in pyrotechnics and also for quick tests on these substances in minerals etc., see e.g the Wikipedia "Flame test".

Lithium: Crimson
Sodium:intense orange-yellow
Potassium:Lilac
Calcium:Red-orange
Strontium:Crimson
Barium:Light green
Copper:Blue-green
Boron:Bright green
LithiumBoronCopperCalcium
(Photos: Herge. The images have been taken from "wikimedia commons" and are reduced in size.)

The spectra which, after the one of hydrogen, are the simplest to explain, are those of the alkali metals. These atoms have a single, relatively weakly bound electron in the outermost shell in addition to the spherical, noble-gas like core. The transitions of the outer electron from the low lying excited states to the ground state produce the visible part of the spectrum.

The sodium spectrum is dominated by a line of 589 nm wavelength, coming from the transition from the 3p state to the 3s state. (In fact, due to fine structure splitting of the p state, which has not been dealt with here, this line is actually a doublet, i.e. two very closely neighbouring lines.)

sodium

"Flame spektrum" of sodium. Scale: wavelength in nm. Data from: Sansonetti and Martin, Handbook of Basic Atomic Spectroscopic Data
If there are more than one electron in the outermost shell, there are many more possibilities of electronic transitions and the spectra accordingly become more involved.


"Flame spektrum" of Calcium. (Only the stronger lines are shown.) Scale: wavelength in nm. Data source as above
Most elements give no conspicuous colour to flames. If the valence electrons are more strongly bound, the energies of the lowest excitations correspond to the ultraviolet region; the strongest spectral lines therefore are invisible for us.

Lightnings


Lightnings. Left: Photo © Axel Rouvin, (source) enlarge.     Right: Photo: Imac Vincent, May 14, 2008. ( source) enlarge.

In lightnings the molecules of the air (nitrogen, oxygen and water vapour) are dissociated and the atoms ionized and excited. The emitted light is white due to the many lines in the visible spectrun, see the figures below. In addition to the lines of nitrogen and oxygen those of hydrogen are present. The varying "red" contribution of the latter (depending on the amount of rain falling or on the density of the clouds) causes the slight differences in observed colour. A lightning spectrum is shown in an "Optics Picture Of the Day" (OPOD) of Les Cowley's Atmospheric Optics site.



Top: Spectrum of atomic nitrogen N und ions N+.
Bottom: Spectrum of oxygen O (two lines in the red region) and O+ (the blue and purple lines). (Only the stronger lines are shown.) Scale: wavelengths in nm. Data source as above.

Coupling rules, "allowed" and "forbidden" transitions

The dominant spectral lines of the polar light belong to atomic oxygen with wavelengths of 558 nm (green) and 630 nm (red). In the above figure these lines are not present at all!
Consider the electron configuration of oxygen: the nucleus carries eight units of positive charge; adding electrons successively to the lowest possible single-particle levels, one reaches the following configuration:
8O:  1s2, 2s2, 2p4.

The four 2p-electrons may be distributed over six possible single-particle states. If there were no interaction between the electrons, all the fifteen possibilities would lead to the same energy. But due to their charge, the electrons repel each other.

Elektrons with parallel spins tend to avoid each other due to the Paiuli principle. Thus, parallel spins are energetically favoured. The larger the total orbital angular momentum, the less is the mutual overlap of the electron densities. This leads to a level splitting according to total orbital angular momentum ("gross structure"). In addition, there is an interaction between orbital and spin-angular momentum, leading to additional splitting according to total angular momentum ("fine structure"). For the lighter elements, spin-orbit interaction is only small. As long as there is no preferred direction in space, total angular momentum is conserved and the states can be labelled by its quantum numbers.

Usually total angular momentum is denoted by capital letters S, P, D, F . . .  standing for L=0, 1, 2, 3  . .  respectively. Spin is given as a left upper index (2S+1).
Thus the lowest few levels of oxygen are the following (experimental data taken from the compilation of Sansonetti und Martin):


 Configuration Term  J  Level (cm−1)
1s2 2s2 2p43P20.000
1158.265
0226.977
1s2 2s2 2p41D215867.862
1s2 2s2 2p41S033792.583
1s2 2s2 2p3(4S)3s5S273768.200
 . . . 
In the Levels' column the energies divided by h·c are given (h being the Planck constant and c the velocity of light). This is very convenient for the computation of the wavelength λ of the spectral lines, as
1/λ = ν/c = (Ei – Ef)/(hc)

For the transition 1S→1D one gets the wavelength of 558 nm – that is the green line, and for 1D→3P the wavelength is 630 nm, the red line of the aurora. But why are these lines not seen under laboratory conditions?

In the treatment of dyes emission and absorption probabilities are dealt with in some nore detail. Large probabilities are only found in electric dipole transitions; transitions which occur much less frequent have been called "forbidden" since the early days of atomic spectroscopy, as often they are not observable at all.

In that sense, both transitions are "forbidden". 1S→1D is an electric quadrupole transition, and in 1D→3P a spin-flip occurs.


As mentioned in the beginning, light emission from single atoms can be observed only seldom in nature. Lightnings and polar lights are the only prominent earthly examples, but if seen, they are impressive!

Polar light (aurora borealis and australis)

Northern (and southern) light is caused by the charged particles (protons and electrons mostly) of the solar wind. The earth's magnetic field forces them on curved paths around the earth, but a fraction is captured and eventually reaches the ionosphere. The details are quite complicated, see the pages of the Atmospheric Optics and the COMET® (Meteorology Education and Training) websites.

Left: Northern light, October 22, 2001, 22:00 UT, as seen north of Wiesbaden, Germany enlarge.
Right: Northern light, October 30, 2003, 19:57 Uhr UT, close to Wolfsheim (Rheinhessen, Germany) enlarge.
Both Photos: © Ulrich Rieth; shown with permission.

Currents of energetic charged particles are flowing at high altitude along the magnetic field lines (the single particles following coiled paths). They come closest to the ground at high latidudes. In collisions, energy is transferred to the particles of the upper atmosphere and is then radiated off as visible light. The polar light originates from heights between roughly 100 and 200 km; in times of strong solar activity also much higher, then it can be seen even at middle latitudes. The composition of the atmosphere at these heights is very different from that of the lower layers: nitrogen molecules and oxygen atoms are much more abundant than all the rest.

The red line of oxygen (630 nm) is dominant at high altitudes, but fades below 150 km, as the excited oxygen atoms in the 1D-state are de-excited by collisions with nitrogen molecules much faster than by radiation. The green colour of the aurora below 150 km height stems from the 558 nm line of Oxygen. It is not seen at larger heights since the 1S-state is not reached from the 3P ground state in collisions with electrons or protons. It is assumed that this state is produced in collisions of O(3P) with excited nitrogen molecules which give off their energy and take over angular momentum:

N2* + O(3P) → N2 + O(1S)
This line vanishes at high altitudes where the concentration of N2 is too low.

Northern light, February 22, 2001, 0:14 UT, Finland close to the polar circle enlarge.
Photo: © Ulrich Rieth.

The following two diagrams are included to substantiate what has been said above. The source of this material is the COMET® Website at http://meted.ucar.edu/ of the University Corporation for Atmospheric Research (UCAR), sponsored in part through cooperative agreement(s) with the National Oceanic and Atmospheric Administration (NOAA), U.S. Department of Commerce (DOC). ©1997-2009 University Corporation for Atmospheric Research. All Rights Reserved.
The animation of this and the next picture does not work if the Adobe Flash Player is not installed. You may click here to open a small page which will test this and guide you to install it.


The composition of the thermosphere (atmosphere above 100 km height). Between 100 and 200 km molecular nitrogen and atomic oxygen are the most abundant. © UCAR, source: COMET® site.

Typical spectrum of (greenish) polar light. By removing or setting checkmarks the different components can be identified. © UCAR, source: COMET® site.
The units of the left scale are kR (kiloRayleigh). These units do not measure perceptual lightness, but the number of photons per unit area and time. The apparently strong lines below 400 nm (4000 Å) and above 700 nm (7000 Å) are hardly visible (and those between 670 and 700 nm are only very faint).
As seen from the above figure, molecular nitrogen can emit blue, red and thus also purple light, and quite multicoloured displays are possible. However, a detailed discussion would lead us too far; see the Atmospheric Optics site for more details and wonderful images.

Gas tubes

Far more often than in natural phenomena one can see artificially induced atomic emission – at least in the city. Here as an example a neon-filled gas discharge tube in front of a black wall is shown. (This and the next picture show exhibits of the "Universum® Science Centre" in Bremen.)

Plasma lamps, plasma balls

  Plasma lamps, invented by Nicola Tesla, have been re-invented as decorative objects, plasma spheres or balls, by Bill Parker. They contain a rarefied noble gas or mixture of noble gases; the energy to excite the atoms is supplied by high frequency high voltage at the inner electrode (ca. 2 kV or more depending on the size, ca. 10–40 kHz). Typical gas pressures range from 2 to 10 Torr. The ball shown to the left presumably contains a mixture of Neon and Xenon (95% Ne, 5% Xe ist customary), other mixtures produce streamers in different colours (for more information see an article in the Chemical and Engineering News).


Molecules

It has already been mentioned that under normal terrestrial conditions only the noble gases consist of single atoms. All other elements have the tendency that their atoms bind to other ones, forming molecules, the energy of which is lower than that of the separate constituents.

In general, the charge distribution in a compound molecule of different atoms is not symmetric, an electric dipole moment results, the molecules attract each other and thus condense to a liquid or a solid.

Small molecules built from the lighter elements are colourless. As the free atoms, they cannot absorb visible light; only in the ultraviolet region the photons have sufficient energy to electronically excite the molecule. On the other hand, the vibrational excitations of the molecules lead to absorption and emission of infrared radiation and causes only very faint colour, as in water.

The large and strongly coloured molecules shall be treated in the special section "dyes", another section is devoted to the colours of minerals and crystals.



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