Information about the International System of Units – the SI – including their definitions using fundamental constants.

This interactive provides information about the International System of Units – the SI. It covers what each unit measures, how it has been defined using fundamental constants and brief insights as to why the constants were chosen. The videos include discussion prompts. Click on the labels for text and videos.

Background image reproduced with permission of the BIPM, which retains full internationally protected copyright, © BIPM.

This resource was created with the assistance of the Measurement Standards Laboratory of New Zealand.

## Transcript

## SI base units

The International System of Units (the SI) is made up of seven universally recognised units of measurement. Some of the units – the kilogram and the metre – we use every day. Other measurements are useful for industrial and scientific needs. On 20 May 2019, four of the base units were redefined based on fixed values for natural constants.

**Discussion point:** Why do you think the measurements are referred to as base units?

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## The candela

The candela (cd) defines luminous intensity (kukū whakaputa tūrama).

The candela was a unit first defined by the amount of light emitted by a common candle, and it is the only SI unit that has a definition based around human perception. It is used to measure the effectiveness of lighting systems made for the human eye.

The SI definition for the candela is the luminous intensity in a given direction of a source that emits monochromatic radiation of frequency 540 × 10^{12} hertz and that has a radiant intensity in that direction of 1/683 watts per steradian (W/sr).

In other words, the candela describes how bright a source of light will be when looking directly at it from a particular direction. There are a number of other – often more useful – photometric quantities than can be measured. These include illuminance (measured in lux), which describes how bright a surface illuminated by a source will be, and luminous flux (measured in lumens), which quantifies the amount of visible light emitted by a source.

**Point of discussion:** The candela is the only SI unit that is tied to human perception. Part of the definition (540 x 10^{12 }Hz) refers to visible green light. Why do you think this frequency was chosen?

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## The kilogram

The kilogram (kg) defines mass (papatipu).

Until 20 May 2019, the kilogram was defined by a physical artefact – a cylinder of platinum-iridium, known as the international prototype kilogram (IPK) – but over time, there was a mass divergence between the IPK and its official copies. The international metrology community agreed that a new definition was needed – one based on a natural constant that wouldn’t change over time.

Now, the kilogram is defined in terms of Planck’s constant (*h*) – a term that links the amount of energy a photon carries with the frequency of its electromagnetic wave. The value of *h* has been fixed to equal 6.626 070 15 x 10^{–34} kg m^{2} s^{–1}. The metre (m) and the second (s) are already defined in terms of fundamental constants – the speed of light and the transition frequency of a caesium atom, respectively. This link allows metrologists to accurately express the kilogram in terms of *h*.

**Discussion point:** Farzana says that the IPK is drifting. What does this mean?

NOTE: This video was filmed prior to the change to SI definitions. As of 20 May 2019, the kilogram is now defined by Planck’s constant rather than the IPK.

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## The metre

The metre (m) defines length (roa).

The metre is defined using a fundamental constant of nature – the speed of light (c), which is given a fixed numerical value of 299,792,458 m s^{-1}, so a metre can be defined as the distance covered by light in a vacuum in exactly 1/299,792,458 of a second.

The definition also relies on another fundamental constant – the frequency of a ^{133}Cs atom (represented as Δν_{Cs}), which has a fixed value of 9 192 631 770 Hz (or s^{-1}).

**Discussion point:** The metre has gone from being defined by a physical artefact, to waves of light from a krypton atom, to a fraction of the speed of light. Do you think that this definition will last – or will we redefine it again?

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## The mole

The mole (mol) defines the amount of substance (rahinga matū).

The definition of the mole was very slightly changed in 2019. It used to be the amount of substance that contains as many chemical units (atoms, molecules or other particles) as there are atoms in exactly 12 grams of carbon-12 (i.e. 6.023 X 10^{23}), exploiting the fact that measuring mass is a useful way to count large numbers of very small things.

The value of the Avogadro number (N_{A}) was fixed at 6.022 140 76 x 10^{23} mol^{–1} as part of the SI revision. One mole is now defined as the amount of substance of a system that contains 6.022 140 76 x 10^{23} specified elementary entities.

**Discussion point: **Mole Day is an unofficial holiday celebrated by scientists. The date is October 23 and the holiday begins at 6.02 am. Why has this date and time been chosen?

NOTE: This video was filmed prior to the change to SI definitions. As of 20 May 2019, the mole is now defined using the Avogadro number instead of 12 grams of carbon-12.

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## The second

The second (s) defines time (wā).

Caesium atomic clocks operate by exposing caesium atoms to microwaves until they start to respond at one of their transition frequencies. By determining this frequency (Δν_{Cs}), an unchanging measurement of time can be established. Δν_{Cs} has a fixed numerical value of 9,192,631,770 Hz, which leads to the following official definition: One second is equal to the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the unperturbed ground state of the ^{133}Cs atom.

Caesium clocks are very stable and are accurate to 1 second every 30 billion years.

**Discussion point:** GPS satellites have onboard caesium and rubidium atomic clocks. What role does time play in how GPS systems work?

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## The kelvin

The kelvin (K) defines thermodynamic temperature (pāmahana wera ahupūngao).

The kelvin used to be defined in relation to the triple point of water – the specific thermodynamic temperature at which the three phases of water (solid ice, liquid water and gaseous water vapour) co-exist (0.01°C or 273.16 K at a pressure of 611.73 Pa).

Now, the definition of temperature is linked to the Boltzmann constant (k), which relates the average relative kinetic energy of particles in a gas with the temperature of the gas. It has a fixed value of 1.380 649 x 10^{–23} J K^{–1}. The joule (J) is a unit equivalent to kg m^{2 }s^{–2}, and all of these units (the kilogram, metre and second) are traceable back to fundamental constants. By fixing k, we can be confident that our definition of temperature will remain consistent.

One kelvin is equal to the change of thermodynamic temperature that results in a change of thermal energy k T by 1.380 649 x 10^{–23} J.

Discussion point: Temperature scales can be relative or absolute. A relative temperature scale measures amounts that are more or less than a reference amount, using positive and negative numbers. An absolute temperature scale uses the value zero as the lowest limit of temperature. How do the commonly used measurements of Celsius, Fahrenheit and Kelvin fit into this?

NOTE: This video was filmed prior to the change to SI definitions. As of 20 May 2019, kelvin is now defined in terms of the Boltzmann constant rather than the triple point of water.

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## The ampere

The ampere (A) defines electric current (iahiko).

The ampere was once defined as the current flowing in two very long parallel wires that are 1 m apart and which gives rise to a magnetic force per unit length of 2 x 10^{-7} N/m.

Like many of the other SI units, the ampere’s definition was updated in May 2019. Now it is linked to the elementary charge (e), which is the electric charge carried by a single electron – e has a fixed value of 1.602 176 634 x 10^{–19} coulomb.

The coulomb can be rewritten as the ampere-second (A s), with s defined by the transition frequency of a caesium atom. This link allows one ampere to be defined solely in terms of fundamental constants – it is the electric current corresponding to the flow of 1/(1.602 176 634 x 10^{–19}) elementary charges per second.

**Discussion point: **The electron charge constant (e) is extraordinarily small. On the positive side, the ampere is defined by a constant. What might be some difficulties in using such a small constant?

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## Acknowledgement

This resource has been updated with the assistance of the Measurement Standards Laboratory of New Zealand.