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temperature and wavelength

glowing and burning

orbits and currents


glowing and burning
In a gas, photons will be emitted in the process of energy reductions of individual electrons. The wavelengths of such photons can only have a limited number of discrete values, each value being related to a certain type of energy transition (see ultraviolet emission). In a solid comparable transitions of individual electrons can take place but more often the exchange of energy is done by vibrational changes of atoms within the grid they are bound in. The type and intensity of these vibrations will change with the amount of applied or expelled energy. Increasing the applied energy will cause transitions from vibrations with a lower level of energy to vibrations with a higher level of energy. The material will release its energy with opposing transitions from higher to lower levels of energy and a simultaneous release of photons. As long as the quantity of supplied energy is relatively low, the wavelength of the emitted photons will be in the long wave infrared area. As we have seen in the previous paragraph, the frequency of a photon is proportional to the amount of released energy while the wavelength is inversely proportional, all according the relation E = hf = hc/λ. The product hc is a constant so by increasing levels of energy the wavelength of the emitted radiation will become shorter and after passing the short wave infrared area it finally will turn into red. This is the point from were the solid will

start emitting light in addition to an already substantial amount of infrared radiation (not to be confused with heat, see infrared radiation). With further increasing levels of energy the frequency of the radiation will shift towards yellow and even blue while the intensity of the light increases, the result being the bright yellow/white light we are familiar with

from incandescent lamps. In an incandescent lamp the energy is supplied to a filament by adding a potential U (with unit volt and symbol V) over the ends of the filament. This causes an electric current I (with unit ampere and symbol A) to flow through the filament. The size of the current is determined by the strength of the binding forces between the electrons and the atoms or molecules of the filament's material. Stronger binding forces result in less current at the same potential while weaker forces result in a higher current. Lets now assume that a voltage U over the ends of the filament will cause a current I to flow through the filament. When the voltage U will be increased to U', the current I will increase from I to I'. The quotient U/I is called the resistance R of the material and a straight resistance is independent of external properties like current, voltage, pressure or temperature. In that case U/I equals U'/I' and the deducted relation U = I*R is known as Ohm's law: "The current through a conductor between two points is directly proportional to the potential difference across the two points". The resistance R is a proportional number with unit volt per ampere (V/A). Instead of V/A commonly the unit Ohm with symbol Ω is used and the resistance of a conductive wire with a given cross-section can than be expressed in Ohms per meter (Ω/m). In reality the resistance of the filament of an incandescent lamp is not linear since it depends strongly on the temperature of the filament. With increasing temperatures the resistance will increase too. When an incandescent lamp is switched on, the temperature of the filament is still relatively low and the current as a result will be high (this is why incandescent lamps mostly fail at the moment they are switched on). The supplied energy will cause the temperature of the filament to rise almost instantly, which increases the resistance and reduces the initial current. After a short while the circuit stabilises and current and temperature will remain constant. The power P (with unit Watt) which is now developed in the filament is proportional to both voltage and current: P = U x I Watt. The amount of energy E that is developed during a period t is proportional to power and time: E = P x t

Wattsecond or Joule. Through a 230 volts, 40 Watt incandescent lamp a current of 174 mA (40 W = 230 V x 0,174 A) will flow in steady state. An amount of energy of 40 Joule per second is than applied to the filament and when properly dimensioned this energy will be sufficient to bring a large number of atoms into vibration. This energy is than released again in a continuous process of relaxation of individual atoms, releasing their energy in the form of photons each time a vibration returns to a lower energy level. The lamp lights up.

infrared emission

extralight/sun substitutes/ infrared emission

atoms and molecules

atoms and molecules
This site is all about the generation of light, infrared- and ultraviolet radiation with help of electricity in order to create an artificial sun substitute. This goal may be obtained by heating up a solid by sending an electric current through it until it glows. It also may be obtained by producing an arc discharge or by a combination of both processes. In order to describe and understand the principles of a heat-lamp or a sun-lamp it is therefore essential to have a common understanding of the phenomena "electric current". Beware however that all the models that will be used further on are only a strong simplification of physical reality and serve mainly to clarify the magic of electricity and radiation within the context of heat- and sun-lamps. Basically, an electric current is a displacement of small electric charges. In a solid, the carriers of such charges are negatively charged electrons who, together with evenly strong but positively charged protons and chargeless neutrons, form atoms, the building blocks of all matter that our earth consists of. Protons and neutrons form the nucleus of an atom while the electrons are circling around this nucleus at a

relatively great distance. The figure next to here depicts this configuration on a non-linear scale. A proton and a neutron are each about 1800 times heavier than an electron and the proper distance between the nucleus and the electrons is much larger than suggested in the figure. When the nucleus would be assumed to have the size of a tennis-ball, the distance towards its nearest electron would be about the height of the Empire State Building. The chargeless

neutrons within the nucleus are preventing the protons to repel each other like the equally named poles of a magnet would do. The number of protons within the nucleus determines the nature of the atom and more than a hundred different atoms are known today. These atoms or elements are depicted with a letter or a combination of letters such as C for carbon, Cu for copper, W for tungsten and Hg for mercury. The smallest element is that of hydrogen (H) with only one proton and one electron. The nucleus of an atom carbon has of six protons while copper has twenty-nine, tungsten seventy-four and mercury eighty. Normally the number of electrons circling the nucleus equals the number of protons within the nucleus, keeping the resulting charge of the atom to be zero. Within solids there is interference between the outer electrons of adjacent atoms and these electrons force the individual atoms to stay in a fixed grid. At higher temperatures the movements within the atoms increases and the forces keeping the grid together decrease as well, causing the material to melt and eventually vaporise. The strength of the binding forces depends on temperature and is different for each element. Copper already melts at a temperature of 1083 ºC while pure tungsten only melts at about 3400 ºC. Mercury is the only metal that is liquid at room temperature and it vaporises at a temperature as low as 357 ºC. Elements may also bind themselves with elements of a different type, thus forming molecules. The properties of molecules differ

from that of the composing atoms or elements. Water for instance consists of two atoms hydrogen (H) and one atom oxygen (O). The elements hydrogen and oxygen both are gasses at room temperature and atmospheric pressure but bound together in a molecule of water they form a liquid under the same circumstances. Together, molecules of the same type form a certain type of material with unique properties and by definition a molecule thus

is the smallest part of material that still has all the properties of that material. Molecules in turn can bind themselves to molecules of different compositions, again creating a new material with unique properties. Glass for instance consists of a complex composition of molecules silicon oxide, sodium oxide, potassium oxide and calcium oxide but there exists no such thing as a molecule of glass.

orbits and currents
The distance at which electrons circle around their nucleus is not arbitrary but limited to a number of fixed orbits, also called bands or subshells. The first subshell (the K-orbit in X-ray notation) can contain two electrons at the utmost. For the second subshell (the L-orbit) this maximum is eight, for the third (the M-orbit) it is eighteen and the N- and O-orbits can contain a maximum of thirty-two electrons each. The outer subshells (the P- and Q-orbits) can contain eighteen, respectively eight electrons. Normally electrons can only be present in an outer subshell when most of the inner subshells are filled up until their maximum. Carbon for instance

contains two electrons in the K-orbit and four in the L-orbit. With mercury the K- until the N-orbit are filled up completely while the O- and P-orbits contain eighteen, respectively two electrons bringing the total to eighty, equal to the number of protons within the nucleus. With electrically conductive solids the outer subshell (the conduction band) is not completely filled until its maximum. This enables individual electrons in the conduction band to travel more or less freely

to the conduction bands of neighbouring atoms. Since the average electron distribution stays the same there is, despite the electron movements, no resulting electric current. When a potential difference is imposed upon the outer ends of a conductor however, the free moving electrons in the conduction bands will attempt to neutralise the potential difference by moving towards the direction of the positive potential. By definition it is than stated that there is a current flowing from the positive potential towards the negative potential although the actual electron movement is just the other way. This confusion finds his origin in the early

Joule. 1 Joule corresponds with 1 Watt during 1 second so in one minute a 40-Watt incandescent lamp converts 40Wx60s = 2400 Joule of energy into heat and light. In relation to individual electrons however, the unit Joule turns out to be unmanageable large and therefore often the unit electronVolt (eV) is used instead. One eV is the amount of energy that is required to make an electron overcome a potential difference of one volt. When using electronVolts, the relation E = hf remains unchanged but E is now expressed in eV instead of Joule and since one electronVolt corresponds with 1,602 x 10^-19 Joule, h is transformed to 4,136 x 10^-15 electronVoltseconde (eVs). An energy transition of 1,24 eV than results in an electromagnetic radiation with a frequency of f = E/h = 1,24 eV/(4,136 x 10^-15) eVs or about 300.000 GHz. The wavelength of this radiation follows from the equation λ = c/f in which λ is the wavelength in meters, f the frequency in Hertz (Hz) or vibrations per second and c is the speed of light, about 300.000 km/s. 300.000 GHz than turns out to be infrared radiation (IR-A) with a wavelength of λ = c/f = 1000nm (see electromagnetic spectrum).

particles and wavelengths

particles and wavelengths
The energy of individual electrons increases with the distance from their nucleus so it takes energy to bring an electron from a lower to a higher band or to knock it out of its highest band. In a conductive solid the electrons in the outer (conductive) bands jump from one nucleus to another but since they effectively remain in the same band this requires a relatively small amount of energy. There are circumstances however that may force an electron to move from a lower to a higher band. Such an electron is said to be excited. Within a gas the binding forces between individual atoms is relatively small and electrons can quite easily be forced to leave their initial orbit, for instance in a collision between two atoms or between an atom and an already freed electron (see ultraviolet emission). An electron that is excited in such a collision and moves from a lower to a higher orbit or even leaves its nucleus completely, absorbs energy in the process of the collision. When the electron escapes from its nucleus it leaves an incomplete atom behind which than becomes positively charged. Such an atom is called an ion. In the opposing relaxation process when an electron returns to an ion or descends from a higher to a lower orbit, it expels the energy it absorbed before. The amount of energy absorbed or expelled in a transition differs per level and per element but is always the same for a certain type of transition. An electron that expels energy does so in the form of small packets- or quanta of energy that are called photons. Photons hence are carriers of energy and they neither posses charge nor mass. Their physical behaviour is partly that of particles and partly that of waves or radiation. The theoretical existence of photons as an

explanation for long known physical observations was predicted by Albert Einstein since the first years of the 20th century and practically proved afterwards. The wave- and radiation characteristics of a photon depends on the energy transition of the related electron according Planck's law: E = hf. In this formula E is the amount of expelled energy in Joule, f is the frequency of the emitted (electromagnetic) radiation in Hertz and h equals 6,626 x 10^-34 Joulesecond (Js), being Planck's constant. In daily life it is quite easy to imagine the unit


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temperature and wavelength
The number of possible types of energy transitions of an electron in material of a given composition is limited and so are the wavelengths of the corresponding photons. The emission of photons by a glowing solid however is mainly the result of vibrational transitions. Like with energy transitions the number of possible vibrational transitions within a solid is limited too but the number of possible variations is far much greater. For this reason the emission spectrum of a glowing solid lacks the existence of the well-defined peaks that often can be seen in the spectrum of hot gasses. A glowing solid is said to have a continuous emission spectrum although there is a more or less clear maximum around a certain wavelength. In 1893 Wilhelm Wien discovered that the wavelength λmax of this maximum is inversely proportional to the absolute temperature T of the glowing solid. The relation λmax = b/T is known as Wien's displacement law. In this formula the temperature T is given in degrees Kelvin (K) instead of Celsius (ºC). Both scales have the same size degree but the definition of their zero-points is different for both scales. For Celsius the zero-point is the temperature of melting ice, for Kelvin it is the lowest temperature that theoretically can exist within the universe, absolute zero. The difference in temperature between these two reference values is 273 ºC so 0K corresponds with -273 ºC while 1000 ºC corresponds with 1273K. The constant b in the formula has a value of 2,898 x 10^-3 Kelvinmeter and is called Wien's constant. Wien identified the temperature-depended displacement of the peak in the emission spectrum of a glowing solid in 1893. The formula for the total emission spectrum has only been deduced

in 1901 by Max Planck. In the figure next to here the emission spectrum of a thermally black body is plotted at different temperatures. A perfect thermally black body absorbs all of the incoming radiation and does not reflect any of it. The emitted radiation than totally depends on the temperature of the body itself. The total amount of radiated energy E* in Watts per square meter happens to be proportional to the fourth power of the temperature of the

body according the relation E* = εσT^4. This formula had been deduced already in 1884 and is called Stefan-Boltzmann's law. In this formula, T again is the temperature of the body in Kelvin and σ is the so-called Stefan-Boltzmann constant being 5,67 x 10^-8 W/m^2.K^4. The radiation factor ε has no dimension and it indicates to which degree a certain body is a perfect thermally black body. The radiation factor therefore is always smaller than one and for a non-perfect black body all values of the characteristics are proportionally lower while the relative distribution of the wavelengths of the radiation roughly stays the same. The temperature of the filament of an incandescent lamp for lighting purposes is about 2800K. For heat-lamps a shift of the radiation peak-level towards the infrared area is desirable and one might expect the temperature of the filament of a heat-lamp to be lower than that of an incandescent lamp. For a great number of heat-lamps, as used for instance in drying-kilns or incubators, this indeed is the case. These lamps operate at a filament temperature of about 2200K and their light production is lower than that of incandescent lamps for lighting purposes while their lifetime can be much longer. From medical experiments it is know that infrared radiation of about 1200 nanometers is the most effective in pain relief. The corresponding temperature for the filament than should be about 2400K. Since the total emission of energy happens to be proportional to the fourth power of the temperature however, it turns out to be effective to increase the temperature of the filament as high as possible and filter out the surplus of visible light. The total quantity of radiation of a filament of 2900K for instance is about two times as high as that of a filament of 2400K and also the relative contribution of short wave infrared radiation increases with temperature. Therefore, as a result of the increased filament temperature, the absolute quantity of infrared radiation in the desired wavelength area is increased significantly. Of course there is an increase in the light component which is even greater but optical filtering can easily reduce this. The maximum temperature of the filament is limited by the properties of the material it is made of. With increasing energy not only the intensity of the vibrational transitions increases but also the energy transitions of individual electrons. At sufficiently high levels of energy, a part of these electrons will leave the filament and finally even entire atoms will escape from the grid and react with the surrounding gasses. The presence of a vacuum around the filament or an environment with inert gasses without any possibility of electric conduction will permit the temperature of the filament to climb just below the melting point of the material. For pure tungsten this melting point is around 3700K, sufficient to withstand the high temperatures required for therapeutic heat-lamps. The price for the higher temperature and the increase in infrared radiation is a shortening of the lifetime of such a lamp. The lifetime of therapeutic heat-lamps is therefore always a compromise with the desired high temperatures and in practice it is limited to about 300 to 500 burning hours were the lifetime for an ordinary incandescent lamp for lighting purposes is in the order of a 1000 hours. For comparison: the earlier described infrared lamps operating at low temperatures can have a lifetime of 3- to even 5000 burning hours.


experiments of Benjamin Franklin who first defined the flow direction of an electric current without completely understanding the mechanism behind it. The effective speed at which electrons travel through a conductor is much smaller than often assumed, that is in the order of a millimeter per second. An electric current of ten ampere for instance, represents an electron displacement of about 6 x 10^19 electrons per second at which the symbol ^ stands for "to the power of". 10^19 is a short notation for a one with nineteen zeros or 10

billion billion. This seems to be a lot of electrons but a copper wire with a cross-cut of one square millimeter and a length of one meter contains about 10^23 copper atoms, as much as the number of tennis balls that would fit into the moon. When we assume that one atom of copper participating in the conduction provides no more than one free electron, the effective drift velocity of the electric charge through the wire would be about (6 x 10^19)/( 10^23) meter/second or 0,6 mm/second. What ìs fast however, is the propagation of a current change. For copper this propagation speed is about 250.000 km/sec so a change in current travels around the globe in about 160 milliseconds. This explains why we can make a fixed wire phone call towards the other side of the earth without any noticeable delay.


electrical conduction (