planck constant - wikipedia, the free encyclopedia

7/29/2019 Planck Constant - Wikipedia, The Free Encyclopedia

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Values ofh Units Ref.

6.626 069 57(29) 1034 Js [1]

4.135 667 516(91) 1015

eVs[1]

2 EPtP

Values of Units Ref.

1.054 571 726(47) 1034 Js [1]

6.582 119 28(15) 1016 eVs [1]

1 EPtP def

Values ofhc Units Ref.

1.986 445 68 1025 Jm

1.239 841 93 eVm

2 EPP

Plaque at the Humboldt University of

Berlin: "Max Planck, discoverer of the

elementary quantum of action h,

taught in this building from 1889 to

1928."

Planck constantFrom Wikipedia, the free encyclopedia

The Planck constant (denoted h, also called Planck'sconstant) is a physical constant that is the quantum of action inquantum mechanics. The Planck constant was first described asthe proportionality constant between the energy (E) of a photonand the frequency () of its associated electromagnetic wave.This relation between the energy and frequency is called thePlanck relation:

Since the frequency , wavelength, and speed of light c arerelated by = c, the Planck relation for a photon can also beexpressed as

The above equation leads to another relationship involving thePlanck constant. Givenp for the linear momentum of a particle,the de Broglie wavelength of the particle is given by

In applications where frequency is expressed in terms of radians persecond ("angular frequency") instead of cycles per second, it is oftenuseful to absorb a factor of 2 into the Planck constant. The resultingconstant is called thereduced PlanckconstantorDirac constant. Itis equal to the Planck constant divided by 2, and is denoted ("h-bar"):

The energy of a photon with angular frequency , where = 2, isgiven by

The reduced Planck constant is the quantum of angular momentum inquantum mechanics.
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The Planck constant is named after Max Planck, the founder of quantum theory, who discovered it in 1900, andwho coined the term "Quantum". Classical statistical mechanics requires the existence ofh (but does not define itsvalue).[2] Planck discovered that physical action could not take on any indiscriminate value. Instead, the actionmust be some multiple of a very small quantity (later to be named the "quantum of action" and now calledPlanck's constant). This inherent granularity is counterintuitive in the everyday world, where it is possible to "makethings a little bit hotter" or "move things a little bit faster". This is because the quanta of action are very, very smallin comparison to everyday macroscopic human experience. Hence, the granularity of nature appears smooth to

us.Thus, on the macroscopic scale, quantum mechanics and classical physics converge at the classical limit.

Nevertheless, it is impossible, as Planck discovered, to explain some phenomena without accepting the fact thataction is quantized. In many cases, such as for monochromatic light or for atoms, this quantum of action alsoimplies that only certain energy levels are allowed, and values in-between are forbidden.[3] In 1923, Louis deBroglie generalized the Planck relation by postulating that the Planck constant represents the proportionality

between the momentum and the quantum wavelength of not just the photon, but the quantum wavelength of anyparticle. This was confirmed by experiments soon afterwards.

Contents

1 Value2 Significance of the value3 Origins

3.1 Black-body radiation3.2 Photoelectric effect3.3 Atomic structure

3.4 Uncertainty principle4 Dependent physical constants

4.1 Rest mass of the electron4.2 Avogadro constant4.3 Elementary charge4.4 Bohr magneton and nuclear magneton

5 Determination5.1 Josephson constant5.2 Watt balance5.3 Magnetic resonance5.4 Faraday constant5.5 X-ray crystal density5.6 Particle accelerator

6 Fixation7 See also8 Notes9 References10 External links

Value

See also: New SI definitions
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The Planck constant of action has the dimensionality of specific relative angular momentum (areal momentum) orangular momentum's intensity. In SI units, the Planck constant is expressed in joule seconds (Js) or (Nms).

The value of the Planck constant is:[1]

The value of the reduced Planck constant is:

The two digits inside the parentheses denote the standard uncertainty in the last two digits of the value. Thefigures cited here are the 2010 CODATA recommended values for the constants and their uncertainties. The2010 CODATA results were made available in June 2011[4] and represent the best-known, internationally-accepted values for these constants, based on all data available as of 2010. New CODATA figures arescheduled to be published approximately every four years.

Significance of the value

The Planck constant is related to the quantization of light and matter. Therefore, the Planck constant can be seenas a subatomic-scale constant. In a unit system adapted to subatomic scales, the electronvolt is the appropriateunit of energy and the Petahertz the appropriate unit of frequency. Atomic unit systems are based (in part) on thePlanck's constant.

The numerical value of the Planck constant depends entirely on the system of units used to measure it. When it isexpressed in SI units, it is one of the smallest constants used in physics. This reflects the fact that on a scale

adapted to humans, where energies are typically of the order of kilojoules and times are typically of the order ofseconds or minutes, Planck's constant (the quantum of action) is very small.

Equivalently, the smallness of Planck's constant reflects the fact that everyday objects and systems are made of alarge number of particles. For example, green light with a wavelength of 555 nanometres (the approximatewavelength to which human eyes are most sensitive) has a frequency of 540 THz (540 1012 Hz). Each photonhas an energyEofh = 3.58 1019 J. That is a very small amount of energy in terms of everyday experience,

but everyday experience is not concerned with individual photons any more than with individual atoms ormolecules. An amount of light compatible with everyday experience is the energy of one mole of photons; itsenergy can be calculated by multiplying the photon energy by the Avogadro constant,NA 6.022 10

23 mol1.

The result is that green light of wavelength 555 nm has an energy of 216 kJ/mol, a typical energy of everyday life.

Origins

Black-body radiation

Main article: Planck's law

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first

posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glowbrighter than cooler ones. The reason is that the electromagnetic field obeys laws of motion just like a mass on aspring, and can come to thermal equilibrium with hot atoms. When a hot object is in equilibrium with light, theamount of light it absorbs is equal to the amount of light it emits. If the object is black, meaning it absorbs all thelight that hits it, then it emits the maximum amount of thermal light too.
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Intensity of light emitted from a black body

at any given frequency. Each color is a

different temperature. Planck was the first

to explain the shape of these curves.

The assumption that blackbody radiation is thermal leads to an accurate prediction: the total amount of emittedenergy goes up with the temperature according to a definite rule, the StefanBoltzmann law (187984). But itwas also known that the colour of the light given off by a hot object changes with the temperature, so that "whitehot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the

peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each differenttemperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximationfor the spectrum of the object, which was correct at high

frequencies (short wavelength) but not at low frequencies (longwavelength).[5] It still was not clearwhy the spectrum of a hotobject had the form that it has (see diagram).

Planck hypothesized that the equations of motion for light are a setof harmonic oscillators, one for each possible frequency. Heexamined how the entropy of the oscillators varied with thetemperature of the body, trying to match Wien's law, and wasable to derive an approximate mathematical function for black-

body spectrum.[6]

However, Planck soon realized that his solution was not unique.There were several different solutions, each of which gave adifferent value for the entropy of the oscillators.[6] To save histheory, Planck had to resort to using the then controversial theoryof statistical mechanics,[6] which he described as "an act ofdespair I was ready to sacrifice any of my previous convictionsabout physics."[7] One of his new boundary conditions was

to interpret UN [the v ibrational energy of N oscillators] not as a continuous, infinitely divisible

quantity, but as a discrete quantity composed of an integral number of finite equal parts. Let us calleach such part the energy element ;

Planck, On the Law of Distribution of Energy in the Normal Spectrum[6]

With this new condition, Planck had imposed the quantization of the energy of the oscillators, "a purely formalassumption actually I did not think much about it" in his own words, [8] but one which would revolutionize

physics. Applying this new approach to Wien's displacement law showed that the "energy element" must beproportional to the frequency of the oscillator, the first version of what is now termed "Planck's relation":

Planck was able to calculate the value ofh from experimental data on black-body radiation: his result,6.55 1034 Js, is within 1.2% of the currently accepted value.[6] He was also able to make the firstdetermination of the Boltzmann constant kB from the same data and theory.

[9]
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Note that the (black) Raleigh-Jeans curve never touches the

Planck curve.

Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever thatit was a continuous variable. The Rayleigh-Jeans law makes close predictions for a narrow range of values at onelimit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck'slaw, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by acomplex factor that involves h in both the numerator and the denominator. The influence ofh in this complexfactor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's lawthat would reproduce the Rayleigh-Jeans law could not be done by changing the values ofh, of the Boltzmann

constant, or of any other constant or variable in the equation. In this case the picture given by classical physics isnot duplicated by a range of results in the quantum picture.

The black-body problem was revisited in 1905,when Rayleigh and Jeans (on the one hand) andEinstein (on the other hand) independently

proved that classical electromagnetism couldneveraccount for the observed spectrum. These

proofs are commonly known as the "ultravioletcatastrophe", a name coined by Paul Ehrenfest in1911. They contributed greatly (along withEinstein's work on the photoelectric effect) toconvincing physicists that Planck's postulate ofquantized energy levels was more than a meremathematical formalism. The very first SolvayConference in 1911 was devoted to "the theoryof radiation and quanta".[10] Max Planckreceived the 1918 Nobel Prize in Physics "inrecognition of the services he rendered to theadvancement of Physics by his discovery of

energy quanta".

Photoelectric effect

Main article: Photoelectric effect

The photoelectric effect is the emission of electrons (called "photoelectrons") from a surface when light is shoneon it. It was first observed by Alexandre Edmond Becquerel in 1839, although credit is usually reserved forHeinrich Hertz,[11] who published the first thorough investigation in 1887. Another particularly thoroughinvestigation was published by Philipp Lenard in 1902.[12] Einstein's 1905 paper[13] discussing the effect in terms

of light quanta would earn him the Nobel Prize in 1921,[11] when his predictions had been confirmed by theexperimental work of Robert Andrews Millikan.[14] The Nobel committee awarded the prize for his work on the

photo-electric effect, rather than relativity, both because of a bias against purely theoretical physics not groundedin discovery or experiment, and dissent amongst its members as to the actual proof that relativity was real.[15]

Prior to Einstein's paper, electromagnetic radiation such as visible light was considered to behave as a wave:hence the use of the terms "frequency" and "wavelength" to characterise different types of radiation. The energytransferred by a wave in a given time is called its intensity. The light from a theatre spotlight is more intense thanthe light from a domestic lightbulb; that is to say that the spotlight gives out more energy per unit time (and henceconsumes more electricity) than the ordinary bulb, even though the colour of the light might be very similar. Otherwaves, such as sound or the waves crashing against a seafront, also have their own intensity. However the energyaccount of the photoelectric effect didn't seem to agree with the wave description of light.
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A schematization of the Bohr model

of the hydrogen atom. The transition

shown from the n=3 level to the n=2level gives rise to visible light of

wavelength 656 nm (red), as the

model predicts .

The "photoelectrons" emitted as a result of the photoelectric effect have a certain kinetic energy, which can bemeasured. This kinetic energy (for each photoelectron) is independentof the intensity of the light,[12] butdepends linearly on the frequency;[14] and if the frequency is too low (corresponding to a kinetic energy for the

photoelectrons of zero or less), no photoelectrons are emitted at all, unless a plurality of photons, whoseenergetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect)[16] Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light sourcecauses more photoelectrons to be emitted with the same kinetic energy, rather than the same number of

photoelectrons to be emitted with higher kinetic energy.[12]

Einstein's explanation for these observations was that light itself is quantized; that the energy of light is nottransferred continuously as in a classical wave, but only in small "packets" or quanta. The size of these "packets"of energy, which would later be named photons, was to be the same as Planck's "energy element", giving themodern version of Planck's relation:

Einstein's postulate was later proven experimentally: the constant of proportionality between the frequency of

incident light () and the kinetic energy of photoelectrons (E) was shown to be equal to the Planck constant(h).[14]

Atomic structure

Main article: Bohr model

Niels Bohr introduced the first quantized model of the atom in 1913, inan attempt to overcome a major shortcoming of Rutherford's classicalmodel.[17] In classical electrodynamics, a charge moving in a circle

should radiate electromagnetic radiation. If that charge were to be anelectron orbiting a nucleus, the radiation would cause it to lose energyand spiral down into the nucleus. Bohr solved this paradox with explicitreference to Planck's work: an electron in a Bohr atom could only havecertain defined energiesEn

where C0 is the speed of light in vacuum,R is an experimentally-

determined constant (the Rydberg constant) and n is any integer (n =1, 2, 3, ). Once the electron reached the lowest energy level (n = 1),it could not get any closer to the nucleus (lower energy). This approachalso allowed Bohr to account for the Rydberg formula, an empiricaldescription of the atomic spectrum of hydrogen, and to account for thevalue of the Rydberg constantR in terms of other fundamental constants.

Bohr also introduced the quantity h/2, now known as the reduced Planck constant, as the quantum of angularmomentum. At first, Bohr thought that this was the angular momentum of each electron in an atom: this provedincorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular

momentum proved beyond the Bohr model. The correct quantization rules for electrons in which the energyreduces to the Bohr-model equation in the case of the hydrogen atom were given by Heisenberg's matrixmechanics in 1925 and the Schrdinger wave equation in 1926: the reduced Planck constant remains the
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fundamental quantum of angular momentum. In modern terms, ifJis the total angular momentum of a system withrotational invariance, andJzthe angular momentum measured along any given direction, these quantities can only

take on the values

Uncertainty principle

Main article: Uncertainty principle

The Planck constant also occurs in statements of Werner Heisenberg's uncertainty principle. Given a largenumber of particles prepared in the same state, the uncertainty in their position, x, and the uncertainty in theirmomentum (in the same direction), p, obey

where the uncertainty is given as the standard deviation of the measured value from its expected value. There area number of other such pairs of physically measurable values which obey a similar rule. One example is time vs.energy. The either-or nature of uncertainty forces measurement attempts to choose between trade offs, and giventhat they are quanta, the trade offs often take the form of either-or (as in Fourier analysis), rather than thecompromises and gray areas of time series analysis.

In addition to some assumptions underlying the interpretation of certain values in the quantum mechanicalformulation, one of the fundamental cornerstones to the entire theory lies in the commutator relationship betweenthe position operator and the momentum operator :

where ij is the Kronecker delta.

Dependent physical constants

The following list is based on the 2006 CODATA evaluation;[18] for the constants listed below, more than 90%of the uncertainty is due to the uncertainty in the value of the Planck constant, as indicated by the square of the

correlation coefficient (r2 > 0.9, r> 0.949). The Planck constant is (with one or two exceptions)[19] thefundamental physical constant which is known to the lowest level of precision, with a relative uncertainty urof

5.0 108.

Rest mass of the electron

The normal textbook derivation of the Rydberg constantR defines it in terms of the electron mass me and avariety of other physical constants.
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However, the Rydberg constant can be determined very accurately (ur= 6.6 1012) from the atomic spectrum

of hydrogen, whereas there is no direct method to measure the mass of a stationary electron in SI units. Hencethe equation for the calculation ofme becomes

where c0 is the speed of light and is the fine-structure constant. The speed of light has an exactly defined valuein SI units, and the fine-structure constant can be determined more accurately (ur= 6.8 10

10) than the Planckconstant: the uncertainty in the value of the electron rest mass is due entirely to the uncertainty in the value of thePlanck constant (r2 > 0.999).

Avogadro constant

Main article: Avogadro constant

The Avogadro constantNA

is determined as the ratio of the mass of one mole of electrons to the mass of a singleelectron: The mass of one mole of electrons is the "relative atomic mass" of an electronAr(e), which can be

measured in a Penning trap (ur= 4.2 1010), multiplied by the molar mass constantMu, which is defined as

0.001 kg/mol.

The dependence of the Avogadro constant on the Planck constant (r2 > 0.999) also holds for the physicalconstants which are related to amount of substance, such as the atomic mass constant. The uncertainty in the

value of the Planck constant limits the knowledge of the masses of atoms and subatomic particles whenexpressed in SI units. It is possible to measure the masses more precisely in atomic mass units, but not to convertthem more precisely into kilograms.

Elementary charge

Main article: Elementary charge

Sommerfeld originally defined the fine-structure constant as:

where e is the elementary charge, 0 is the electric constant (also called the permittivity of free space), and0 isthe magnetic constant (also called the permeability of free space). The latter two constants have fixed values inthe International System of Units. However, can also be determined experimentally, notably by measuring theelectron spin g-factorge, then comparing the result with the value predicted by quantum electrodynamics.

At present, the most precise value for the elementary charge is obtained by rearranging the definition of to

obtain the following definition ofe in terms of and h:
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MethodValue ofh

(1034 Js)

Relative

uncertaintyRef.

Watt balance 6.626 068 89(23) 3.4 108 [20][21][22]

X-ray crystaldensity

6.626 0745(19) 2.9 107 [23]

Josephsonconstant

6.626 0678(27) 4.1 107 [24][25]

Magneticresonance

6.626 0724(57) 8.6 107 [26][27]

Faradayconstant 6.626 0657(88) 1.3 106 [28]

CODATA

2010

recommended

value

6.626 069 57(29) 4.4 108 [1]

The nine recent determinations of the Planck constant coverfive separate methods. Where there is more than one recentdetermination for a given method, the value ofh given here

is a weighted mean of the results, as calculated byCODATA.

Bohr magneton and nuclear magneton

Main articles: Bohr magneton and Nuclear magneton

The Bohr magneton and the nuclear magneton are units which are used to describe the magnetic properties of theelectron and atomic nuclei respectively. The Bohr magneton is the magnetic moment which would be expectedfor an electron if it behaved as a spinning charge according to classical electrodynamics. It is defined in terms of

the reduced Planck constant, the elementary charge and the electron mass, all of which depend on the Planckconstant: the final dependence on h (r2 > 0.995) can be found by expanding the variables.

The nuclear magneton has a similar definition, but corrected for the fact that the proton is much more massivethan the electron. The ratio of the electron relative atomic mass to the proton relative atomic mass can bedetermined experimentally to a high level of precision (ur= 4.3 10

10).

Determination

In principle, the Planck constant could bedetermined by examining the spectrum of a black-

body radiator or the kinetic energy of

photoelectrons, and this is how its value was firstcalculated in the early twentieth century. In practice,these are no longer the most accurate methods. TheCODATA value quoted here is based on threewatt-balance measurements ofKJ

2RKand oneinter-laboratory determination of the molar volumeof silicon,[18] but is mostly determined by a 2007watt-balance measurement made at the U.S.

National Institute of Standards and Technology(NIST).[22] Five other measurements by threedifferent methods were initially considered, but notincluded in the final refinement as they were tooimprecise to affect the result.

There are both practical and theoretical difficulties indetermining h. The practical difficulties can beillustrated by the fact that the two most accuratemethods, the watt balance and the X-ray crystaldensity method, do not appear to agree with oneanother. The most likely reason is that themeasurement uncertainty for one (or both) of themethods has been estimated too low it is (or theyare) not as precise as is currently believed but for

the time being there is no indication which method is at fault.
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The theoretical difficulties arise from the fact that all of the methods exceptthe X-ray crystal density method relyon the theoretical basis of the Josephson effect and the quantum Hall effect. If these theories are slightlyinaccurate though there is no evidence at present to suggest they are the methods would not give accuratevalues for the Planck constant. More importantly, the values of the Planck constant obtained in this way cannot

be used as tests of the theories without falling into a circular argument. Fortunately, there are other statistical waysof testing the theories, and the theories have yet to be refuted. [18]

Josephson constant

The Josephson constantKJ relates the potential difference Ugenerated by the Josephson effect at a "Josephsonunction" with the frequency of the microwave radiation. The theoretical treatment of Josephson effect suggests

very strongly thatKJ = 2e/h.

The Josephson constant may be measured by comparing the potential difference generated by an array of

Josephson junctions with a potential difference which is known in SI volts. The measurement of the potentialdifference in SI units is done by allowing an electrostatic force to cancel out a measurable gravitational force.Assuming the validity of the theoretical treatment of the Josephson effect,KJ is related to the Planck constant by

Watt balance

Main article: Watt balance

A watt balance is an instrument for comparing two powers, one of which is measured in SI watts and the other ofwhich is measured in conventional electrical units. From the definition of the conventionalwatt W90, this gives a

measure of the productKJ2RKin SI units, whereRKis the von Klitzing constant which appears in the quantum

Hall effect. If the theoretical treatments of the Josephson effect and the quantum Hall effect are valid, and inparticular assuming thatRK= h/e

2, the measurement ofKJ2RKis a direct determination of the Planck constant.

Magnetic resonance

Main article: Gyromagnetic ratio

The gyromagnetic ratio is the constant of proportionality between the frequency of nuclear magneticresonance (or electron paramagnetic resonance for electrons) and the applied magnetic fieldB: = B. It isdifficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuringB, but the valuefor protons in water at 25 C is known to better than one part per million. The protons are said to be "shielded"

from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemicalshift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, p. The

gyromagnetic ratio is related to the shielded proton magnetic momentp, the spin numberI(I=12 for protons)

and the reduced Planck constant.
http://en.wikipedia.org/wiki/Spin_numberhttp://en.wikipedia.org/wiki/Chemical_shifthttp://en.wikipedia.org/wiki/Part_per_millionhttp://en.wikipedia.org/wiki/Water_(molecule)http://en.wikipedia.org/wiki/Protonhttp://en.wikipedia.org/wiki/Electron_paramagnetic_resonancehttp://en.wikipedia.org/wiki/Nuclear_magnetic_resonancehttp://en.wikipedia.org/wiki/Gyromagnetic_ratiohttp://en.wikipedia.org/wiki/Quantum_Hall_effecthttp://en.wikipedia.org/wiki/Von_Klitzing_constanthttp://en.wikipedia.org/wiki/Conventional_electrical_unithttp://en.wikipedia.org/wiki/Watthttp://en.wikipedia.org/wiki/Power_(physics)http://en.wikipedia.org/wiki/Watt_balancehttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Josephson_effecthttp://en.wikipedia.org/wiki/Josephson_effect


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The ratio of the shielded proton magnetic momentp to the electron magnetic momente can be measuredseparately and to high precision, as the imprecisely-known value of the applied magnetic field cancels itself out intaking the ratio. The value ofe in Bohr magnetons is also known: it is half the electron g-factorge. Hence

A further complication is that the measurement ofp involves the measurement of an electric current: this isinvariably measured in conventionalamperes rather than in SI amperes, so a conversion factor is required. Thesymbolp-90 is used for the measured gyromagnetic ratio using conventional electrical units. In addition, thereare two methods of measuring the value, a "low-field" method and a "high-field" method, and the conversion

factors are different in the two cases. Only the high-field valuep-90(hi) is of interest in determining the Planckconstant.

Substitution gives the expression for the Planck constant in terms ofp-90(hi):

Faraday constant

Main article: Faraday constant

The Faraday constantFis the charge of one mole of electrons, equal to the Avogadro constantNA multiplied bythe elementary charge e. It can be determined by careful electrolysis experiments, measuring the amount of silverdissolved from an electrode in a given time and for a given electric current. In practice, it is measured inconventional electrical units, and so given the symbolF90. Substituting the definitions ofNA and e, and converting

from conventional electrical units to SI units, gives the relation to the Planck constant.

X-ray crystal density

The X-ray crystal density method is primarily a method for determining the Avogadro constant NA but as theAvogadro constant is related to the Planck constant it also determines a value for h. The principle behind the

method is to determineNA as the ratio between the volume of the unit cell of a crystal, measured by X-raycrystallography, and the molar volume of the substance. Crystals of silicon are used, as they are available in highquality and purity by the technology developed for the semiconductor industry. The unit cell volume is calculatedfrom the spacing between two crystal planes referred to as d220. The molar volume Vm(Si) requires a knowledgeof the density of the crystal and the atomic weight of the silicon used. The Planck constant is given by
http://en.wikipedia.org/wiki/Atomic_weighthttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Semiconductorhttp://en.wikipedia.org/wiki/Siliconhttp://en.wikipedia.org/wiki/Molar_volumehttp://en.wikipedia.org/wiki/X-ray_crystallographyhttp://en.wikipedia.org/wiki/Unit_cellhttp://en.wikipedia.org/wiki/Silverhttp://en.wikipedia.org/wiki/Electrolysishttp://en.wikipedia.org/wiki/Electric_chargehttp://en.wikipedia.org/wiki/Faraday_constanthttp://en.wikipedia.org/wiki/Ampere


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Particle accelerator

The experimental measurement of the Planck constant in the Large Hadron Collider laboratory was carried out in2011. The study called PCC using a giant particle accelerator helped to better understand the relationships

between the Planck constant and measuring distances in space. [needs citation]

Fixation

As mentioned above, the numerical value of the Planck constant depends on the system of units used to describeit. Its value in SI units is known to 50 parts per billion but its value in atomic units is known exactly, because ofthe way the scale of atomic units is defined. The same is true of conventional electrical units, where the Planckconstant (denoted h90 to distinguish it from its value in SI units) is given by

withKJ90 andRK90 being exactly defined constants. Atomic units and conventional electrical units are veryuseful in their respective fields, because the uncertainty in the final result does not depend on an uncertainconversion factor, only on the uncertainty of the measurement itself.

There are a number of proposals to redefine certain of the SI base units in terms of fundamental physicalconstants.[29] This has already been done for the metre, which is defined in terms of a fixed value of the speed oflight. The most urgent unit on the list for redefinition is the kilogram, whose value has been fixed for all science(since 1889) by the mass of a small cylinder of platinumiridium alloy kept in a vault just outside Paris. Whilenobody knows if the mass of the International Prototype Kilogram has changed since 1889 the value 1 kg of itsmass expressed in kilograms is by definition unchanged and therein lies one of the problems it is known thatover such a timescale the many similar PtIr alloy cylinders kept in national laboratories around the world, havechanged their relative mass by several tens of parts per million, however carefully they are stored, and the moreso the more they have been taken out and used as mass standards. A change of several tens of micrograms inone kilogram is equivalent to the current uncertainty in the value of the Planck constant in SI units.

The legal process to change the definition of the kilogram is already underway,[29] but it was decided that no finaldecision would be made before the next meeting of the General Conference on Weights and Measures in2011.[30] The Planck constant is a leading contender to form the basis of the new definition, although not the onlyone.[30] Possible new definitions include "the mass of a body at rest whose equivalent energy equals the energy of

photons whose frequencies sum to 135,639,274 1042 Hz",[31] or simply "the kilogram is defined so that thePlanck constant equals 6.626 068 96 1034 Js".

The BIPM providedDraft Resolution A in anticipation of the 24th General Conference on Weights andMeasures meeting (2011-10-17 through 2011-10-21), detailing the considerations "On the possible futurerevision of the International System of Units, the SI".[32]

Watt balances already measure mass in terms of the Planck constant: at present, standard mass is taken as fixedand the measurement is performed to determine the Planck constant but, were the Planck constant to be fixed inSI units, the same experiment would be a measurement of the mass. The relative uncertainty in the measurementwould remain the same.
http://en.wikipedia.org/wiki/Watt_balancehttp://en.wikipedia.org/wiki/BIPMhttp://en.wikipedia.org/wiki/General_Conference_on_Weights_and_Measureshttp://en.wikipedia.org/wiki/International_Prototype_Kilogramhttp://en.wikipedia.org/wiki/Iridiumhttp://en.wikipedia.org/wiki/Platinumhttp://en.wikipedia.org/wiki/Kilogramhttp://en.wikipedia.org/wiki/SI_base_unithttp://en.wikipedia.org/wiki/Parts_per_billionhttp://en.wikipedia.org/wiki/Large_Hadron_Collider


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Mass standards could also be constructed from silicon crystals or by other atom-counting methods. Suchmethods require a knowledge of the Avogadro constant, which fixes the proportionality between atomic massand macroscopic mass but, with a defined value of the Planck constant,NA would be known to the same level ofuncertainty (if not better) than current methods of comparing macroscopic mass.

See also

New SI definitionsBasic concepts of quantum mechanicsPlanck unitsStigler's lawWaveparticle duality

Notes

1. ^a

b

c

d

e

f

P.J. Mohr, B.N. Taylor, and D.B. Newell (2011), "The 2010 CODATA Recommended Values of theFundamental Physical Constants" (Web Version 6.0). This database was developed by J. Baker, M. Douma, andS. Kotochigova. Available: http://physics.nist.gov (http://physics.nist.gov/cgi-bin/cuu/Results?search_for=planck) [Thursday, 02-Jun-2011 21:00:12 EDT]. National Institute of Standards and Technology,Gaithersburg, MD 20899.

2. ^ Giuseppe Morandi, F. Napoli, E. Ercolessi (2001), Statistical mechanics: an intermediate course(http://books.google.com/?id=MhInFlnNsREC&pg=PA51&lpg=PA51&dq=celestial+mechanics+planck+constant#v=onepage&q=celestial%20mechanics%20planck%20constant&f=false), ISBN 978-981-02-4477-4, "See page 85"

3. ^ Einstein, Albert (2003), "Physics and Reality" (http://www.kostic.niu.edu/Physics_and_Reality-Albert_Einstein.pdf), Daedalus132 (4): 24, doi:10.1162/001152603771338742

(http://dx.doi.org/10.1162%2F001152603771338742), "The question is first: How can one assign a discretesuccession of energy value H to a system specified in the sense of classical mechanics (the energy function is agiven function of the coordinates qrand the corresponding momenta pr)? Planck's constant h relates thefrequencyH/h to the energy values H. It is therefore sufficient to give to the system a succession of discretefrequency values."

4. ^ "CODATA recommended values" (http://physics.nist.gov/cuu/Reference/versioncon.shtml).5. ^ R. Bowley, M. Snchez (1999),Introductory Statistical Mechanics (2nd ed.), Oxford: Clarendon Press,

ISBN 0-19-850576-0

6. ^ abcde Planck, Max (1901), "Ueber das Gesetz der Energieverteilung im Normalspectrum"(http://www.physik.uni-augsburg.de/annalen/history/historic-papers/1901_309_553-563.pdf), Ann. Phys.309(3): 55363, Bibcode:1901AnP...309..553P (http://adsabs.harvard.edu/abs/1901AnP...309..553P),

doi:10.1002/andp.19013090310 (http://dx.doi.org/10.1002%2Fandp.19013090310). English translation: "On theLaw of Distribution of Energy in the Normal Spectrum (http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html)".

7. ^ Kragh, Helge (1 December 2000),Max Planck: the reluctant revolutionary(http://physicsworld.com/cws/article/print/373), PhysicsWorld.com

8. ^ Kragh, Helge (1999), Quantum Generations: A History of Physics in the Twentieth Century(http://books.google.com/?id=ELrFDIldlawC&printsec=frontcover), Princeton University Press, p. 62, ISBN 0-691-09552-3

9. ^ Planck, Max (2 June 1920), The Genesis and Present State of Development of the Quantum Theory (NobelLecture) (http://nobelprize.org/nobel_prizes/physics/laureates/1918/planck-lecture.html)

10. ^Previous Solvay Conferences on Physics(http://www.solvayinstitutes.be/Conseils%20Solvay/PreviousPhysics.html), International Solvay Institutes,retrieved 12 December 2008

11. ^ ab See, e.g., Arrhenius, Svante (10 December 1922), Presentation speech of the 1921 Nobel Prize for Physics(http://nobelprize.org/nobel_prizes/physics/laureates/1921/press.html)

12. ^ abc Lenard, P. (1902), "Ueber die lichtelektrische Wirkung", Ann. Phys.313 (5): 14998,
http://en.wikipedia.org/wiki/Annalen_der_Physikhttp://en.wikipedia.org/wiki/Philipp_Lenardhttp://nobelprize.org/nobel_prizes/physics/laureates/1921/press.htmlhttp://en.wikipedia.org/wiki/Svante_Arrheniushttp://www.solvayinstitutes.be/Conseils%20Solvay/PreviousPhysics.htmlhttp://nobelprize.org/nobel_prizes/physics/laureates/1918/planck-lecture.htmlhttp://en.wikipedia.org/wiki/Max_Planckhttp://en.wikipedia.org/wiki/Special:BookSources/0-691-09552-3http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://books.google.com/?id=ELrFDIldlawC&printsec=frontcoverhttp://physicsworld.com/cws/article/print/373http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.htmlhttp://dx.doi.org/10.1002%2Fandp.19013090310http://en.wikipedia.org/wiki/Digital_object_identifierhttp://adsabs.harvard.edu/abs/1901AnP...309..553Phttp://en.wikipedia.org/wiki/Bibcodehttp://en.wikipedia.org/wiki/Annalen_der_Physikhttp://www.physik.uni-augsburg.de/annalen/history/historic-papers/1901_309_553-563.pdfhttp://en.wikipedia.org/wiki/Max_Planckhttp://en.wikipedia.org/wiki/Special:BookSources/0-19-850576-0http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://physics.nist.gov/cuu/Reference/versioncon.shtmlhttp://dx.doi.org/10.1162%2F001152603771338742http://en.wikipedia.org/wiki/Digital_object_identifierhttp://www.kostic.niu.edu/Physics_and_Reality-Albert_Einstein.pdfhttp://en.wikipedia.org/wiki/Special:BookSources/978-981-02-4477-4http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://books.google.com/?id=MhInFlnNsREC&pg=PA51&lpg=PA51&dq=celestial+mechanics+planck+constant#v=onepage&q=celestial%20mechanics%20planck%20constant&f=falsehttp://physics.nist.gov/cgi-bin/cuu/Results?search_for=planckhttp://en.wikipedia.org/wiki/Wave%E2%80%93particle_dualityhttp://en.wikipedia.org/wiki/Stigler%27s_lawhttp://en.wikipedia.org/wiki/Planck_unitshttp://en.wikipedia.org/wiki/Basic_concepts_of_quantum_mechanicshttp://en.wikipedia.org/wiki/New_SI_definitionshttp://en.wikipedia.org/wiki/Atomic_mass


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Bibcode:1902AnP...313..149L (http://adsabs.harvard.edu/abs/1902AnP...313..149L),doi:10.1002/andp.19023130510 (http://dx.doi.org/10.1002%2Fandp.19023130510)

13. ^ Einstein, Albert (1905), "ber einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischenGesichtspunkt" (http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1905_17_132-148.pdf),Ann. Phys.17 (6): 13248, Bibcode:1905AnP...322..132E (http://adsabs.harvard.edu/abs/1905AnP...322..132E),doi:10.1002/andp.19053220607 (http://dx.doi.org/10.1002%2Fandp.19053220607)

14. ^ abc Millikan, R. A. (1916), "A Direct Photoelectric Determination of Planck's h",Phys. Rev.7 (3): 35588,Bibcode:1916PhRv....7..355M (http://adsabs.harvard.edu/abs/1916PhRv....7..355M),

doi:10.1103/PhysRev.7.355 (http://dx.doi.org/10.1103%2FPhysRev.7.355)15. ^ Einstein, His Life and Universe, Walter Isaacson, pp. 309314.16. ^ Smith, Richard (1962), "Two Photon Photoelectric Effect", Physical Review128 (5): 2225,

Bibcode:1962PhRv..128.2225S (http://adsabs.harvard.edu/abs/1962PhRv..128.2225S),doi:10.1103/PhysRev.128.2225 (http://dx.doi.org/10.1103%2FPhysRev.128.2225).Smith, Richard (1963),"Two-Photon Photoelectric Effect",Physical Review130 (6): 2599, Bibcode:1963PhRv..130.2599S(http://adsabs.harvard.edu/abs/1963PhRv..130.2599S), doi:10.1103/PhysRev.130.2599.4(http://dx.doi.org/10.1103%2FPhysRev.130.2599.4).

17. ^ Bohr, Niels (1913), "On the Constitution of Atoms and Molecules", Phil. Mag., Ser. 626 (153): 125,doi:10.1080/14786441308634993 (http://dx.doi.org/10.1080%2F14786441308634993)

18. ^ abc Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). "CODATA Recommended Values of the

Fundamental Physical Constants: 2006" (http://physics.nist.gov/cuu/Constants/index.html).Rev. Mod. Phys.80(2): 633730. arXiv:0801.0028 (http://arxiv.org/abs/0801.0028). Bibcode:2008RvMP...80..633M(http://adsabs.harvard.edu/abs/2008RvMP...80..633M). doi:10.1103/RevModPhys.80.633(http://dx.doi.org/10.1103%2FRevModPhys.80.633). Direct link to value (http://physics.nist.gov/cgi-bin/cuu/Value?h).

19. ^ The main exceptions are the Newtonian constant of gravitation G and the gas constantR. The uncertainty inthe value of the gas constant also affects those physical constants which are related to it, such as the Boltzmannconstant and the Loschmidt constant.

20. ^ Kibble, B P; Robinson, I A; Belliss, J H (1990), "A Realization of the SI Watt by the NPL Moving-coilBalance",Metrologia27 (4): 17392, Bibcode:1990Metro..27..173K(http://adsabs.harvard.edu/abs/1990Metro..27..173K), doi:10.1088/0026-1394/27/4/002(http://dx.doi.org/10.1088%2F0026-1394%2F27%2F4%2F002)

21. ^ Steiner, R.; Newell, D.; Williams, E. (2005), "Details of the 1998 Watt Balance Experiment Determining thePlanck Constant" (http://nvl.nist.gov/pub/nistpubs/jres/110/1/j110-1ste.pdf),Journal of Research (NationalInstitute of Standards and Technology) 110 (1): 126

22. ^ ab Steiner, Richard L.; Williams, Edwin R.; Liu, Ruimin; Newell, David B. (2007), "Uncertainty Improvementsof the NIST Electronic Kilogram", IEEE Transactions on Instrumentation and Measurement56 (2): 59296,doi:10.1109/TIM.2007.890590 (http://dx.doi.org/10.1109%2FTIM.2007.890590)

23. ^ Fujii, K.; Waseda, A.; Kuramoto, N.; Mizushima, S.; Becker, P.; Bettin, H.; Nicolaus, A.; Kuetgens, U. et al.(2005), "Present state of the avogadro constant determination from silicon crystals with natural isotopiccompositions",IEEE Transactions on Instrumentation and Measurement54 (2): 85459,

doi:10.1109/TIM.2004.843101 (http://dx.doi.org/10.1109%2FTIM.2004.843101) |displayauthors= suggested(help)24. ^ Sienknecht, Volkmar; Funck, Torsten (1985), "Determination of the SI Volt at the PTB", IEEE Trans.

Instrum. Meas.34 (2): 19598, doi:10.1109/TIM.1985.4315300(http://dx.doi.org/10.1109%2FTIM.1985.4315300). Sienknecht, V; Funck, T (1986), "Realization of the SI UnitVolt by Means of a Voltage Balance",Metrologia22 (3): 20912, Bibcode:1986Metro..22..209S(http://adsabs.harvard.edu/abs/1986Metro..22..209S), doi:10.1088/0026-1394/22/3/018(http://dx.doi.org/10.1088%2F0026-1394%2F22%2F3%2F018). Funck, T.; Sienknecht, V. (1991),"Determination of the volt with the improved PTB voltage balance", IEEE Transactions on Instrumentation andMeasurement40 (2): 15861, doi:10.1109/TIM.1990.1032905(http://dx.doi.org/10.1109%2FTIM.1990.1032905)

25. ^ Clothier, W. K.; Sloggett, G. J.; Bairnsfather, H.; Currey, M. F.; Benjamin, D. J. (1989), "A Determination ofthe Volt",Metrologia26 (1): 946, Bibcode:1989Metro..26....9C(http://adsabs.harvard.edu/abs/1989Metro..26....9C), doi:10.1088/0026-1394/26/1/003(http://dx.doi.org/10.1088%2F0026-1394%2F26%2F1%2F003)

26. ^ Kibble, B P; Hunt, G J (1979), "A Measurement of the Gyromagnetic Ratio of the Proton in a Strong Magnetic"
http://adsabs.harvard.edu/abs/1979Metro..15....5Khttp://en.wikipedia.org/wiki/Bibcodehttp://en.wikipedia.org/wiki/Metrologiahttp://dx.doi.org/10.1088%2F0026-1394%2F26%2F1%2F003http://en.wikipedia.org/wiki/Digital_object_identifierhttp://adsabs.harvard.edu/abs/1989Metro..26....9Chttp://en.wikipedia.org/wiki/Bibcodehttp://en.wikipedia.org/wiki/Metrologiahttp://dx.doi.org/10.1109%2FTIM.1990.1032905http://en.wikipedia.org/wiki/Digital_object_identifierhttp://dx.doi.org/10.1088%2F0026-1394%2F22%2F3%2F018http://en.wikipedia.org/wiki/Digital_object_identifierhttp://adsabs.harvard.edu/abs/1986Metro..22..209Shttp://en.wikipedia.org/wiki/Bibcodehttp://en.wikipedia.org/wiki/Metrologiahttp://dx.doi.org/10.1109%2FTIM.1985.4315300http://en.wikipedia.org/wiki/Digital_object_identifierhttp://en.wikipedia.org/wiki/Help:CS1_errors#displayauthorshttp://dx.doi.org/10.1109%2FTIM.2004.843101http://en.wikipedia.org/wiki/Digital_object_identifierhttp://dx.doi.org/10.1109%2FTIM.2007.890590http://en.wikipedia.org/wiki/Digital_object_identifierhttp://nvl.nist.gov/pub/nistpubs/jres/110/1/j110-1ste.pdfhttp://dx.doi.org/10.1088%2F0026-1394%2F27%2F4%2F002http://en.wikipedia.org/wiki/Digital_object_identifierhttp://adsabs.harvard.edu/abs/1990Metro..27..173Khttp://en.wikipedia.org/wiki/Bibcodehttp://en.wikipedia.org/wiki/Metrologiahttp://en.wikipedia.org/wiki/Loschmidt_constanthttp://en.wikipedia.org/wiki/Boltzmann_constanthttp://en.wikipedia.org/wiki/Gas_constanthttp://en.wikipedia.org/wiki/Newtonian_constant_of_gravitationhttp://physics.nist.gov/cgi-bin/cuu/Value?hhttp://dx.doi.org/10.1103%2FRevModPhys.80.633http://en.wikipedia.org/wiki/Digital_object_identifierhttp://adsabs.harvard.edu/abs/2008RvMP...80..633Mhttp://en.wikipedia.org/wiki/Bibcodehttp://arxiv.org/abs/0801.0028http://en.wikipedia.org/wiki/ArXivhttp://en.wikipedia.org/wiki/Reviews_of_Modern_Physicshttp://physics.nist.gov/cuu/Constants/index.htmlhttp://dx.doi.org/10.1080%2F14786441308634993http://en.wikipedia.org/wiki/Digital_object_identifierhttp://en.wikipedia.org/wiki/Philosophical_Magazinehttp://en.wikipedia.org/wiki/Niels_Bohrhttp://dx.doi.org/10.1103%2FPhysRev.130.2599.4http://en.wikipedia.org/wiki/Digital_object_identifierhttp://adsabs.harvard.edu/abs/1963PhRv..130.2599Shttp://en.wikipedia.org/wiki/Bibcodehttp://dx.doi.org/10.1103%2FPhysRev.128.2225http://en.wikipedia.org/wiki/Digital_object_identifierhttp://adsabs.harvard.edu/abs/1962PhRv..128.2225Shttp://en.wikipedia.org/wiki/Bibcodehttp://dx.doi.org/10.1103%2FPhysRev.7.355http://en.wikipedia.org/wiki/Digital_object_identifierhttp://adsabs.harvard.edu/abs/1916PhRv....7..355Mhttp://en.wikipedia.org/wiki/Bibcodehttp://en.wikipedia.org/wiki/Physical_Reviewhttp://en.wikipedia.org/wiki/Robert_Andrews_Millikanhttp://dx.doi.org/10.1002%2Fandp.19053220607http://en.wikipedia.org/wiki/Digital_object_identifierhttp://adsabs.harvard.edu/abs/1905AnP...322..132Ehttp://en.wikipedia.org/wiki/Bibcodehttp://en.wikipedia.org/wiki/Annalen_der_Physikhttp://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1905_17_132-148.pdfhttp://en.wikipedia.org/wiki/Albert_Einsteinhttp://dx.doi.org/10.1002%2Fandp.19023130510http://en.wikipedia.org/wiki/Digital_object_identifierhttp://adsabs.harvard.edu/abs/1902AnP...313..149Lhttp://en.wikipedia.org/wiki/Bibcode


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, , .. ....(http://adsabs.harvard.edu/abs/1979Metro..15....5K), doi:10.1088/0026-1394/15/1/002(http://dx.doi.org/10.1088%2F0026-1394%2F15%2F1%2F002)

27. ^ Liu Ruimin; Liu Hengji; Jin Tiruo; Lu Zhirong;Du Xianhe; Xue Shouqing; Kong Jingwen; Yu Baijiang;ZhouXianan; Liu Tiebin; Zhang Wei (1995), "A Recent Determination for the SI Values of p and 2e/h at NIM"(http://en.cnki.com.cn/Article_en/CJFDTOTAL-JLXB503.000.htm),Acta Metrologica Sinica16 (3): 16168

28. ^ Bower, V. E.; Davis, R. S. (1980), "The Electrochemical Equivalent of Pure Silver: A Value of the FaradayConstant" (http://cdm16009.contentdm.oclc.org/cdm/compoundobject/collection/p13011coll6/id/58310/rec/14),Journal of Research (National Bureau Standards) 85 (3): 17591

29. ^ ab 94th Meeting of the International Committee for Weights and Measures (2005). Recommendation 1:Preparative steps towards new definitions of the kilogram, the ampere, the kelvin and the mole in terms offundamental constants (http://www.bipm.org/utils/en/pdf/CIPM2005-EN.pdf)

30. ^ ab 23rd General Conference on Weights and Measures (2007). Resolution 12: On the possible redefinition ofcertain base units of the International System of Units (SI) (http://www.bipm.org/utils/en/pdf/Resol23CGPM-EN.pdf).

31. ^ Taylor, B. N.; Mohr, P. J. (1999), "On the redefinition of the kilogram" (http://www.iop.org/EJ/article/0026-1394/36/1/11/me9111.pdf), Metrologia36 (1): 6364, Bibcode:1999Metro..36...63T(http://adsabs.harvard.edu/abs/1999Metro..36...63T), doi:10.1088/0026-1394/36/1/11(http://dx.doi.org/10.1088%2F0026-1394%2F36%2F1%2F11)

32. ^Draft Resolution A: On the possible future revision of the International System of Units, the SI(http://www.bipm.org/utils/common/pdf/24_CGPM_Convocation_Draft_Resolution_A.pdf)

References

Barrow, John D. (2002), The Constants of Nature; From Alpha to Omega The Numbers thatEncode the Deepest Secrets of the Universe, Pantheon Books, ISBN 0-375-42221-8

External links

Quantum of Action and Quantum of Spin Numericana(http://www.numericana.com/answer/constants.htm#h)Moriarty, Philip; Eaves, Laurence; Merrifield, Michael (2009). "h Planck's Constant"(http://www.sixtysymbols.com/videos/planck.htm). Sixty Symbols. Brady Haran for the University of

Nottingham.

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