BIPM November 2018: New definitions for SI fundamental units

The Committee on Data for Science and Technology (CODATA) publishes values for physical constants for international use. It determines the Avogadro constant from the ratio of the molar mass of the electron to the rest mass of the electron

NA= Ar(e) Mu / me                 where:

Ar(e) = relative atomic mass of electron
NA = Avogadro constant;
Mu = Molar mass constant (kilograms per gram i.e. 1/1000)
me = electron rest mass

The relative atomic mass of the electron, Ar(e), is a directly measured quantity, and the molar mass constant, Mu, is a defined constant in the SI. (to change grams to kilograms)

(The electron rest mass, however, is calculated from other measured constants.

me = 2 R∞ h / c α2                 where:  me = electron rest mass; R∞= Rydberg constant;
h = Plancks constant; c = Speed of light; α = Fine structure constant

me = 9.10938356(11)×10−31 kg)

(Carbon 12C  is taken as the standard atom and has a relative atomic mass (Ar) of 12.

mkg = mu ×1.66053886 * 10-27  and if mu =1/1000 exactly then

1 Relative atomic mass unit = 1.660539E-24

)

As may be observed in the table below, the main limiting factor in the precision of the Avogadro constant is the uncertainty in the value of the Planck constant h, as all the other constants that contribute to the calculation are known more precisely.

Constant

Symbol

2014 CODATA value

Relative standard uncertainty

Proton–electron mass ratio

mp/me

1836.152 673 89(17)

9.5×10–11

Molar mass constant

Mu

0.001 kg/mol = 1 g/mol

0 (defined)

Rydberg constant

R∞

10 973 731.568 508(65) m−1

5.9×10–12

Planck constant

h

6.626 070 040(81)×10–34 J s

1.2×10–8

Speed of light

c

299 792 458 m/s

0 (defined)

Fine structure constant

α

7.297 352 5664(17)×10–3

2.3×10–10

Avogadro constant

NA

6.022 140 857(74)×1023 mol−1

1.2×10–8

The ampere will be defined by the elementary electrical charge – "e" – which is 1.602176634 × 10–19 C

The kelvin will be defined by the Boltzmann constant – "k" – which is 1.380649 × 10–23 J.K–1

Steps towards the new SI unit definitions

The Second

was originally defined as 1/60 of 1/60 of 1/24 of the mean solar day and continued to be so defined through CGS and MKS systems. However development of quartz crystal timekeepers showed up the variation in the mean solar day; so in 1956 the second was redefined as the “ephemeris second”

1s = 1 / 31,556,925.9747 of the tropical year for 1900.  
This definition was adopted for by the SI system (1960); however development of atomic clocks showed a better standard was needed.

Since 1967, the second has been defined as exactly "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" (at a temperature of 0 K). This length of a second was selected to correspond exactly to the length of the ephemeris second previously defined.

Atomic clocks use such a frequency to measure seconds by counting cycles per second at that frequency. Radiation of this kind is one of the most stable and reproducible phenomena of nature. The current generation of atomic clocks are accurate to within one second in a few hundred million years.

However atomic clocks use microwave radiation at 9.2 GHz, so achieving the stabilities of one part in 1015 is only possible by averaging the signal over a period of about a day, which makes it hard to use the fountain clock at this level of accuracy in real time.

With frequencies approaching 1015 Hz – some 100,000 times higher than the 9.2 GHz microwave frequency of the fountain – optical clocks should be stable to almost one part in 1015 simply by averaging over just a few seconds, rather than a day. With longer averaging times, stabilities of one part in 1017 or better should be possible.

So it is likely that in the future the standard will be based on an optical transition.

The metre

Having a new and precise definition for the second allowed the metre to be redefined. The metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole. An inconvenient value!

In 1799, it was redefined in terms of a prototype metre bar of platinum. (the actual bar used was changed in 1889 – the new bar of platinum-iridium with two finely engraved lines “1m” apart at 0 degrees and 1atm pressure.). In 1960, the metre was redefined in terms of a certain number of wavelengths of a certain emission line of krypton-86. In 1983, the current definition was adopted.

The metre is now defined as the distance travelled by light in a vacuum in 1/299 792 458 second.

At this point the definitions for the second and metre had been established in such a way as no longer to need physical exemplars such as the metre bar. However the unit for mass (kilogram) was still defined in such terms.

The kilogram

The gram was originally defined as the mass of 1 cubic centimetre of pure water. This led to a more precise definition for a kilogram as the mass of 1 cubic decimetre of pure water at the temperature of its maximum density (about 4 deg C.)

In 1799, an all-platinum kilogram prototype was fabricated in platinum to replicate this mass, and represent a standard for measurement.( kilogram of the Archives.)

This was replaced in 1889 by a platinum-iridium cylinder (International Prototype of the Kilogram, IPK or “le Grand K), which has 6 “sister copies”, ten “working copies” and many “National prototypes”.

This has remained as the standard until now.  However studies have shown the mass of the IPK has changed by comparison with its sisters and the other prototypes. A new more accessible, more stable, and more precise standard was needed.

The Mole

John Dalton (1805) published a table in which relative atomic mass (aka atomic weight) was described. Hydrogen, Oxygen and Carbon12 have all been used as standards; so for many years the mole was defined as the number of atoms in 12g of  12C.

However the latest definition of the mole (IBPM 2011) was as follows:

“The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram (i.e. 12 grams) of carbon-12.”  (i.e. the Avogadro constant)

“When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.”

Note the mole unusually is specified in grams because of the historical context.

New definitions

Of the seven SI base units (second, metre, kilogram, Ampere, Kelvin, mole, candela) the definitions for the kilogram, Ampere, Kelvin and mole can all now be redefined in terms of universal physical constants.

Having measured these constants by reference to our existing standards the BIPM will

 define them as follows:

The definition for the kg:

The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10−34 J⋅s = kg m2 s−1,

where the metre and the second are defined in terms of c and ΔνCs.

The definition for the Ampere

The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 1.602176634×10−19 Coulombs (= A s),

where the second is defined in terms of Δ ν Cs.

The definition for the Kelvin

The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant k to be 1.380649×10−23 J K-1, = kg m2 s−2 K−1,

where the kilogram, metre and second are defined in terms of h, c and ΔνCs

The definition for the mole

Previous definition: The mole is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12.  New definition: The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.02214076×1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol−1 and is called the Avogadro number.

The candela

In essence this has not been a big change except for the change in the definition of the kilogram. - The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy K of monochromatic radiation of frequency 540×1012 Hz, Kcd, to be 683 when expressed in the unit lm W−1, which is equal to cd sr W−1, or cd sr kg−1 m−2 s3, where the kilogram, metre and second are defined in terms of h, c and ΔνCs.

(A steradian sr is the angle of a conic section of a sphere that has an angle of 1 radian at the apex and encloses an area on the surface of the sphere equal to the radius squared)

References

https://www.labnews.co.uk/features/last-unit-standing-13-07-2017/

https://en.wikipedia.org/wiki/Avogadro_constant

https://www.bipm.org/en/cgpm-2018/

https://physicsworld.com/a/optical-clocks/