SI Base Units

SI Base Units

SI (International System of Units) defines seven base units which are 

• meter
• kilogram
• second
• ampere
• kelvin
• mole
• candela

The definition of the mole, alongside redefinitions of the kilogram, ampere, and kelvin (and candela) were formally approved by the General Conference on Weights and Measures (CGPM) on November 16, 2018, and officially took effect on May 20, 2019 (World Metrology Day).

The base units form the foundation upon which all other units of measurement are built.

• Base Units are Independent Physical Quantities:
  • They represent a distinct and independent physical quantity.
  • They are irreducible dimensions of physical phenomena.

All other units in the SI system are called derived units which are combinations of base units.

I show the base and derived unit relationship in the schematic below for four of these units (time, length, mass, and current). 

Picture – Some SI Base and Derived Units

The derived units shown in the picture above are

• Energy:  1 joule = 1 newton-meter
• Force:  1 newton = 1(kilogram-meter)/(second squared)
• Charge: 1 coulomb = 1 ampere-second
• Power: 1 watt = 1 joule/second
• Voltage: 1 volt = 1 watt/ampere

The SI units all are based on known constants and they are the same everywhere in the universe. 

These constants are:

• c: the speed of light in vacuum: 299,792,458 meters per second.
• h: the Planck constant: Energy is exchanged and absorbed in specific amounts, known as “quanta” and h defines the size of those quanta. It equals  exactly 6.626 070 15 × 10-34 Joule seconds.
• e: elementary charge: e is the amount of charge in an electron and is equal to 1.602176634 x 10^-19 coulombs.
• ∆νCs: the hyperfine transition frequency of cesium-133 = 9,192,631,770 hertz.
• k: the Boltzmann constant relates an object’s energy to its temperature. It equals 1.380649 x 10^-23 joules/kelvin.
• N_A: the Avogadro constant defines the number of particles in a mole and equals 6.02214076 x 10²³  particles per mole.
• K_cd: the luminous efficacy of monochromatic radiation of frequency 540 × 1012 hertz. K_cd is equal to 683 lumens per watt

Specific definitions for the SI base units are provided below. 

Time: second = s

(adopted in 1967): The second is defined as the duration of exactly 9,192,631,770 cycles of the microwave radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

Length: meter = m

• The meter is based on the definition of the speed of light c = 299,792,458 meters per second (or m/s)
• (adopted in 1983): 1 meter is the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second.

Mass: kilogram = kg

(adopted 2019): It is defined by taking the fixed numerical value of the Planck constant h to be 6.626 070 15 x 10^–34 when expressed in the unit J s, which is equal to kg m² s^–1

Current: ampere = A

• Its magnitude is set by fixing the numerical value of the elementary charge to be equal to exactly 1.602176634 x 10^-19 when it is expressed in the SI units As [ampere seconds], which is equal to C (Coulombs).
• (adopted 2019): Per NIST, “The ampere is a measure of the amount of electric charge in motion per unit time ― that is, electric current. But the quantity of electric charge by itself, whether in motion or not, is expressed by another SI unit, the coulomb (C).
• One coulomb is equal to about 6.241 x 10¹⁸ electric charges (e). One ampere is the current in which one coulomb of charge travels across a given point in 1 second.”

Temperature: kelvin = K

• (Adopted 2019): Its magnitude is set by fixing the numerical value of the Boltzmann constant to be equal to exactly 1.380649 x 10^-23 … J/K [joules per kelvin].
• The Boltzmann constant relates an object’s energy to its temperature.
• So a Kelvin is the change of thermodynamic temperature that results in a change of thermal energy by 1.380649x 10^-23 … Joules.

Mole: mol 

• (Adopted 2019): 1 mole contains exactly 6.02214076 x 10²³ elementary particles.
• This number is the fixed numerical value of the Avogadro constant (N_A), when expressed in the unit mol⁻¹ (reciprocal mole), and is called the Avogadro number.
• The “elementary entities” can be atoms, molecules, ions, electrons, any other particle, or specified groups of such particles.

Luminous Intensity: Candela: cd 

• A candela is the SI unit of luminous intensity. 
• (adopted 2019):  Defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 x 10¹² Hz, K_cd , to be exactly 683 when expressed in the unit lm/W (lumen per watt), which is equal to cd⋅sr⋅/W (candela steradian per watt).
• It refers to light at a very specific frequency (540 x 10¹² Hz), which corresponds to green-yellow light, the color to which the human eye is most sensitive under normal daylight conditions.
• The “luminous efficacy” (K_cd) is the conversion factor between the purely physical power of light (measured in watts) and its perceived brightness (measured in lumens).
• By fixing K_cd to 683 lm/W for this specific frequency, the definition essentially establishes the amount of light, as perceived by the average human eye, that corresponds to one candela.