Crookes radiometer
Encyclopedia
The Crookes radiometer, also known as the light mill, consists of an airtight glass bulb, containing a partial vacuum
Vacuum
In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...

. Inside are a set of vanes which are mounted on a spindle. The vanes rotate when exposed to light, with faster rotation for more intense light, providing a quantitative measurement of electromagnetic radiation intensity. The reason for the rotation has historically been a cause of much scientific debate.

It was invented in 1873 by the chemist Sir William Crookes as the by-product of some chemical research. In the course of very accurate quantitative chemical work, he was weighing samples in a partially evacuated chamber to reduce the effect of air currents, and noticed the weighings were disturbed when sunlight shone on the balance. Investigating this effect, he created the device named after him. It is still manufactured and sold as a novelty item.

General description

The radiometer
Radiometer
A radiometer is a device for measuring the radiant flux of electromagnetic radiation. Generally, the term radiometer denotes an infrared radiation detector, yet it also includes detectors operating on any electromagnetic wavelength....

 is made from a glass bulb from which much of the air has been removed to form a partial vacuum
Vacuum
In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...

. Inside the bulb, on a low friction
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...

 spindle, is a rotor with several (usually four) vertical lightweight metal vanes spaced equally around the axis. The vanes are polished or white on one side, black on the other. When exposed to sunlight
Sunlight
Sunlight, in the broad sense, is the total frequency spectrum of electromagnetic radiation given off by the Sun. On Earth, sunlight is filtered through the Earth's atmosphere, and solar radiation is obvious as daylight when the Sun is above the horizon.When the direct solar radiation is not blocked...

, artificial light, or infrared
Infrared
Infrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...

 radiation (even the heat of a hand nearby can be enough), the vanes turn with no apparent motive power, the dark sides retreating from the radiation source and the light sides advancing. Cooling the radiometer causes rotation in the opposite direction.

The effect begins to be seen at partial vacuum pressures of a few torr
Torr
The torr is a non-SI unit of pressure with the ratio of 760 to 1 standard atmosphere, chosen to be roughly equal to the fluid pressure exerted by a millimetre of mercury, i.e., a pressure of 1 torr is approximately equal to 1 mmHg...

 (several hundred pascals), reaches a peak at around 10−2 torr (1 pascal) and has disappeared by the time the vacuum reaches 10−6 torr (10-4 pascal) (see explanations note 1). At these very high vacuums the effect of photon radiation pressure
Radiation pressure
Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic radiation. If absorbed, the pressure is the power flux density divided by the speed of light...

 on the vanes can be observed in very sensitive apparatus (see Nichols radiometer
Nichols radiometer
A Nichols radiometer was the apparatus used by Ernest Fox Nichols and Gordon Ferrie Hull in 1901 for the measurement of radiation pressure. It consisted of a pair of small silvered glass mirrors suspended in the manner of a torsion balance by a fine quartz fibre within an enclosure in which the air...

) but this is insufficient to cause rotation.

The word-element "radio-" in the title originates from the combining form of Latin radius, a ray. Here it refers to electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

. A Crookes radiometer, consistent with the word-element "meter" in its title, can provide a quantitative measurement of electromagnetic radiation intensity. This can be done, for example, by visual means (e.g., a spinning slotted disk, which functions as a simple stroboscope
Stroboscope
A stroboscope, also known as a strobe, is an instrument used to make a cyclically moving object appear to be slow-moving, or stationary. The principle is used for the study of rotating, reciprocating, oscillating or vibrating objects...

) without interfering with the measurement itself.

Radiometers are now commonly sold worldwide as a novelty ornament; needing no batteries, but only light to get the vanes to turn. They come in various forms, such as the one pictured, and are often used in science museum
Science museum
A science museum or a science centre is a museum devoted primarily to science. Older science museums tended to concentrate on static displays of objects related to natural history, paleontology, geology, industry and industrial machinery, etc. Modern trends in museology have broadened the range of...

s to illustrate "radiation pressure
Radiation pressure
Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic radiation. If absorbed, the pressure is the power flux density divided by the speed of light...

" – a scientific principle that they do not in fact demonstrate.

External radiant source motion

When a radiant energy
Radiant energy
Radiant energy is the energy of electromagnetic waves. The quantity of radiant energy may be calculated by integrating radiant flux with respect to time and, like all forms of energy, its SI unit is the joule. The term is used particularly when radiation is emitted by a source into the...

 source is directed at a Crookes radiometer, the radiometer becomes a heat engine
Heat engine
In thermodynamics, a heat engine is a system that performs the conversion of heat or thermal energy to mechanical work. It does this by bringing a working substance from a high temperature state to a lower temperature state. A heat "source" generates thermal energy that brings the working substance...

. The operation of a heat engine is based on a difference in temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

 that is converted to a mechanical output. In this case, the black side of the vane becomes hotter than the other side, as radiant energy from a light source warms the black side by black-body absorption faster than the silver or white side. The internal air molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

s are "heated up" (i.e. experience an increase in their speed) when they touch the black side of the vane. The details of exactly how this moves the hotter side of the vane forward are given in the section below.

The internal temperature rises as the black vanes impart heat to the air molecules, but the molecules are cooled again when they touch the bulb's glass surface, which is at ambient temperature. This heat loss through the glass keeps the internal bulb temperature steady so that the two sides of the vanes can develop a temperature difference. The white or silver side of the vanes are slightly warmer than the internal air temperature but cooler than the black side, as some heat conducts through the vane from the black side. The two sides of each vane must be thermally insulated to some degree so that the silver or white side does not immediately reach the temperature of the black side. If the vanes are made of metal, then the black or white paint can be the insulation. The glass stays much closer to ambient temperature than the temperature reached by the black side of the vanes. The higher external air pressure helps conduct heat away from the glass.

The air pressure inside the bulb needs to strike a balance between too low and too high. A strong vacuum inside the bulb does not permit motion, because there are not enough air molecules to cause the air currents that propel the vanes and transfer heat to the outside before both sides of each vane reach thermal equilibrium by heat conduction through the vane material. High inside pressure inhibits motion because the temperature differences are not enough to push the vanes through the higher concentration of air: there is too much air resistance for "eddy currents" to occur, and any slight air movement caused by the temperature difference is damped by the higher pressure before the currents can "wrap around" to the other side.

Motion without external radiation

When the radiometer is heated in the absence of a light source, it turns in the forward direction (i.e. black sides trailing). If a person's hands are placed around the glass without touching it, the vanes will turn slowly or not at all, but if the glass is touched to warm it quickly, they will turn more noticeably. Directly heated glass gives off enough infrared radiation to turn the vanes, but glass blocks much of the far-infrared radiation from a source of warmth not in contact with it. However, near-infrared and visible light more easily penetrate the glass.

If the glass is cooled quickly in the absence of a strong light source by putting ice on the glass or placing it in the freezer with the door almost closed, it turns backwards (i.e. the silver sides trail). This demonstrates black-body radiation from the black sides of the vanes rather than black-body absorption. The wheel turns backwards because the black sides cool more quickly than the silver sides.

Explanations for the force on the vanes

Over the years, there have been many attempts to explain how a Crookes radiometer works:
  1. Crookes incorrectly suggested that the force was due to the pressure of light
    Radiation pressure
    Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic radiation. If absorbed, the pressure is the power flux density divided by the speed of light...

    . This theory was originally supported by James Clerk Maxwell
    James Clerk Maxwell
    James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...

    , who had predicted this force. This explanation is still often seen in leaflets packaged with the device. The first experiment to disprove this theory was done by Arthur Schuster
    Arthur Schuster
    Sir Franz Arthur Friedrich Schuster FRS was a German-born British physicist known for his work in spectroscopy, electrochemistry, optics, X-radiography and the application of harmonic analysis to physics...

     in 1876, who observed that there was a force on the glass bulb of the Crookes radiometer that was in the opposite direction to the rotation of the vanes. This showed that the force turning the vanes was generated inside the radiometer. If light pressure were the cause of the rotation, then the better the vacuum in the bulb, the less air resistance to movement, and the faster the vanes should spin. In 1901, with a better vacuum pump, Pyotr Lebedev
    Pyotr Nikolaevich Lebedev
    Pyotr Nikolaevich Lebedev was a Russian physicist.He made his doctoral degree in Strasbourg under the supervision of August Kundt in 1887–1891. In 1891 he started working in Moscow State University in the group of Alexander Stoletov. There he made his famous experimental studies of...

     showed that in fact, the radiometer only works when there is low pressure gas in the bulb, and the vanes stay motionless in a hard vacuum. Finally, if light pressure were the motive force, the radiometer would spin in the opposite direction, as the photon
    Photon
    In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

    s on the shiny side being reflected would deposit more momentum than on the black side where the photons are absorbed. The actual pressure exerted by light is far too small to move these vanes, but can be measured with devices such as the Nichols radiometer
    Nichols radiometer
    A Nichols radiometer was the apparatus used by Ernest Fox Nichols and Gordon Ferrie Hull in 1901 for the measurement of radiation pressure. It consisted of a pair of small silvered glass mirrors suspended in the manner of a torsion balance by a fine quartz fibre within an enclosure in which the air...

    .
  2. Another incorrect theory was that the heat on the dark side was causing the material to outgas, which pushed the radiometer around. This was effectively disproved by both Schuster's and Lebedev's experiments.
  3. A partial explanation is that gas molecule
    Molecule
    A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

    s hitting the warmer side of the vane will pick up some of the heat, bouncing off the vane with increased speed. Giving the molecule this extra boost effectively means that a minute pressure is exerted on the vane. The imbalance of this effect between the warmer black side and the cooler silver side means the net pressure on the vane is equivalent to a push on the black side, and as a result the vanes spin round with the black side trailing. The problem with this idea is that while the faster moving molecules produce more force, they also do a better job of stopping other molecules from reaching the vane, so the net force on the vane should be exactly the same — the greater temperature causes a decrease in local density which results in the same force on both sides. Years after this explanation was dismissed, Albert Einstein
    Albert Einstein
    Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

     showed that the two pressures do not cancel out exactly at the edges of the vanes because of the temperature difference there. The force predicted by Einstein would be enough to move the vanes, but not fast enough.
  4. The final piece of the puzzle, thermal transpiration, was theorized by Osborne Reynolds
    Osborne Reynolds
    Osborne Reynolds FRS was a prominent innovator in the understanding of fluid dynamics. Separately, his studies of heat transfer between solids and fluids brought improvements in boiler and condenser design.-Life:...

    , but first published by James Clerk Maxwell
    James Clerk Maxwell
    James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...

     in the last paper before his death in 1879. Reynolds found that if a porous plate is kept hotter on one side than the other, the interactions between gas molecules and the plates are such that gas will flow through from the cooler to the hotter side. The vanes of a typical Crookes radiometer are not porous, but the space past their edges behaves like the pores in Reynolds's plate. On average, the gas molecules move from the cold side toward the hot side whenever the pressure ratio is less than the square root of the (absolute) temperature ratio. The pressure difference causes the vane to move, cold (white) side forward.


Both Einstein's and Reynolds's forces appear to cause a Crookes radiometer to rotate, although it still isn't clear which one is stronger.

All-black light mill

To rotate, a light mill does not have to be coated with different colors across each vane. In 2009, researchers at the University of Texas, Austin created a monocolored light mill which has four curved vanes; each vane forms a convex and a concave surface. The light mill is uniformly coated by gold nanocrystals, which are a strong light absorber. Upon exposure, due to geometric effect, the convex side of the vane receives more photon energy than the concave side does, and subsequently the gas molecules receive more heat from the convex side than from the concave side. At rough vacuum, this asymmetric
Asymmetry
Asymmetry is the absence of, or a violation of, symmetry.-In organisms:Due to how cells divide in organisms, asymmetry in organisms is fairly usual in at least one dimension, with biological symmetry also being common in at least one dimension....

 heating effect generates a net gas movement across each vane, from the concave side to the convex side, as shown by the researchers' Direct Simulation Monte Carlo
Direct simulation Monte Carlo
Direct Simulation Monte Carlo method uses probabilistic simulation to solve the Boltzmann equation for finite Knudsen number fluid flows....

 (DSMC) modeling. The gas movement causes the light mill to rotate with the concave side moving forward, due to Newton's Third Law.
This monocolored design promotes the fabrication of micrometer
Micrometer
A micrometer , sometimes known as a micrometer screw gauge, is a device incorporating a calibrated screw used widely for precise measurement of small distances in mechanical engineering and machining as well as most mechanical trades, along with other metrological instruments such as dial, vernier,...

- or nanometer- scaled light mills, for it is difficult to pattern materials of distinct optical properties within a very narrow, three-dimensional space.

Nanoscale light mill

In 2010 researchers at the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...

 succeeded in building a nanoscale light mill that works on an entirely different principle to the Crookes radiometer. A gammadion shaped gold
Gold
Gold is a chemical element with the symbol Au and an atomic number of 79. Gold is a dense, soft, shiny, malleable and ductile metal. Pure gold has a bright yellow color and luster traditionally considered attractive, which it maintains without oxidizing in air or water. Chemically, gold is a...

 light mill, only 100 nanometers in diameter, was built and illuminated by laser light that had been tuned to have an angular momentum. The possibility of doing this had been suggested by the Princeton physicist Richard Beth in 1936. The torque was greatly enhanced by the resonant coupling of the incident light to plasmonic wave
Surface plasmon
Surface plasmons , are coherent electron oscillations that exist at the interface between any two materials where the real part of the dielectric function changes sign across the interface...

s in the gold structure.

External links

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