Understanding the New SI

Earlier this year, much publicity heralded a change to the way in which the SI unit of mass, the kilogram, was to be redefined. No longer was it to be defined in terms of the ‘international prototype kilogram’, a revered cylindrical metal artifact located in a laboratory in Saint-Cloud in the western suburbs of Paris. Instead, its definition was to be based on an unalterable physical constant: the equivalent mass of the energy of a photon, given its frequency via the Planck constant.

Although most of the publicity surrounded the redefinition of the kilogram, in fact each of the seven SI base units were also affected by changes to their definitions.

Three of the seven SI base units (metre, second, and candela) were already defined in terms of physical constants, so their existing definitions only required minor changes to their wording. However, the remaining four (kilogram, ampere, kelvin, and mole) each required significant revision.

Unfortunately, the scientific jargon used in these new definitions have made them considerably harder for the average student to understand! In fact, it would be fair to say that considerable knowledge of physics would be required for them to make any sense!

It must be understood that these changes represent a major change to the way in which the SI system works, because the seven base units, essentially, have lost their importance in favour of seven physical constants.

These physical constants are:

  • The speed of lightc, is exactly 299 792 458 m/s (metres per second);
  • The ground state hyperfine structure transition frequency of the caesium-133 atomΔνCs , is exactly 919 263 177 0 Hz (hertz);
  • The luminous efficacyKcd , of monochromatic radiation of frequency 540×1012 Hz (540 THz) —a frequency of green-coloured light at approximately the peak sensitivity of the human eye— is exactly 683 lm/W (lumens per watt);
  • The Planck Constant, h, is exactly 6.626 070 15×10−34 J·s (joule-second);
  • The elementary chargeeis exactly 1.602 176 634×10−19 C (coulomb);
  • The Boltzmann Constantk. is exactly 1.380 649×10−23  J/K (joule per kelvin);
  • The Avogadro Constant, NA , is exactly 6.022 140 76×1023  mol−1 (reciprocal mole).

So what exactly are these constants? And what do they mean?

Speed of light: nothing in the cosmos —matter, information, energy, etc. —can travel faster than the speed of light. It helps define the metre, the kilogram, and the kelvin.

Planck Constant: this is one of the fundamental constants used in quantum mechanics, which tells us that energy is exchanged and absorbed in discrete amounts, or ‘packets of energy’, called ‘quanta’. The Planck Constant defines the size of those quanta, expressed in joule seconds. It helps define the kilogram, the kelvin, and the candela.

Elementary Charge: this is the amount of electric charge on an individual electron. It helps define the ampere.

Hyperfine transition frequency of cesium-133: Cesium is a metal atom in the periodic table. Cesium-133 is its most common form, an isotope containing a total of 133 protons and neutrons. The energy of cesium’s outermost (valence) electron can be controlled using microwave radiation. The frequency of the microwave radiation that causes this electron to jump between two closely spaced low-energy states is known as the ‘hyperfine transition frequency’. It helps to define the second, metre, kilogram, and ampere.

Boltzmann constant: this relates an object’s energy to its temperature. It helps to define the kelvin.

Avogadro constant: defines the number of particles in a mole, the SI base unit for the amount of substance. Simply put, Avogadro’s number of electrons equals one mole of electrons. Similarly, Avogadro’s number of water molecules equals one mole of water.

Luminous efficacy, Kcd , of monochromatic radiation of frequency 540×1012 Hzto explain this, let’s start with the second half of the definition. ‘Monochromatic radiation of frequency 540 × 1012 Hz’ is simply the frequency of (green) light to which the human eye is most sensitive. And ‘luminous efficacy’ is the ratio of luminous flux emited by a luminous source to its input power. It helps to define the candela.

New/Revised Definitions of SI Base Units

The metre (symbol: m) is defined by taking the fixed numerical value of the speed of light in vacuum, c, to be 299 792 458 when expressed in the unit metre per second (m/ s), where the second is defined in terms of the constant ∆νCs.

The kilogram (symbol: kg) is defined by taking the fixed numerical value of the Planck constant, h, to be 6.626 070 15 ×10−34 when expressed in the unit joule second (J·s), which is equal to  a kilogram square metre per second (kg·m2 /s), where the metre and the second are defined in terms of the constants c and ∆νCs

The second (symbol: s) is defined by taking the fixed numerical value of the cesium frequency. ∆νCs, the unperturbed ground-state hyperfine transition frequency of the cesium-133 atom, to be 9 192 631 770 when expressed in the unit hertz (Hz), which is equal to s−1.

The ampere (symbol: A)  is defined by taking the fixed numerical value of the elementary charge, e, to be 1.602 176 634 × 10−19 when expressed in the unit coulomb (C), which is equal to ampere second (A·s), where the second is defined in terms of ∆νCs.

The kelvin (symbol: K) is defined by taking the fixed numerical value of the Boltzmann constant, k, to be 1.380 649 ×10−23 when expressed in the unit joule per kelvin (J/K), which is equal to kilogram square metre per square second per kelvin (kg·m2 /s2 ·K), where the kilogram, metre, and second are defined in terms of h, c, and ∆νCs.

The candela (symbol: cd) is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, to be 683 when expressed in the unit lumen per watt (lm W−1), which is equal to candela steridian per watt (cd·sr/W), or cd sr−1 m−2 s3, where the kilogram, metre, and second are defined in terms of h, c and ∆νCs.

A mole (symbol: mol) contains exactly 6.022 140 76 × 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 amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles.

Of particular interest to us is the new definition of the ampere which is significantly different from the one that has been in use since 1948:

The ampere (symbol: A) is defined as that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed one meter apart in vacuum, would produce between these conductors a force equal to 2 × 10−7 newton per metre of length.

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