3.1 The Value of Defined Quantity Is the Quantity Expressed …
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units, which together with the derived units make up a coherent system of units of
measurement. In addition, certain entities outside of the system are accepted for use
with SI units.
The base units of the international system of units (SI):
• The second (s) is the unit of time, defined by fixed numerical value of the caesium
1
frequency Δν Cs , the unperturbed ground-state hyperfine transition frequency of
the caesium 133 atom, at 9,192,631,770 when expressed in the unit Hz, which is
equal to s
−1 .
• The meter (m) is the unit of length, defined by the fixed numerical value of the
speed of light in vacuum, c, at 299,792,458 when expressed in the unit m s
−1 ,
where the second is defined in terms of the caesium frequency Δν Cs .
• The kilogram (kg) is the unit of mass, defined by taking the fixed numerical value
of the Planck constant h to be 6.626070040 × 10
−34 when expressed in the unit
J s, which is equal to kg m
2 s
−1 , where the metre and the second are defined in
terms of c and Δν Cs
• The ampere (A) is the unit of electric current, defined by fixed numerical value
of the elementary charge e at 1.6021766208 × 10
−19 when expressed in the unit
C, which is equal to A s, where the second is in terms of Δν Cs .
• The kelvin (K) is the unit of the thermodynamic temperature, defined by taking
the fixed numerical value of the Boltzmann constant k at 1.38064852 × 10
−23
when expressed in the unit J K
−1 , which is equal to kg m
2 s
−1 K
−1 , where the
kilogram, metre and second are defined in terms of h, c and Δν Cs .
• The mole (mol) is the unit of amount of substance of a specific elementary entity,
which may be an atom, molecule, ion, electron or any other particle or a specified
group of such particles, defined by the fixed numerical value of the Avogadro
constant N A at 6.022408 s57 × 10
23 when expressed in the unit mol
−1 .
• The candela (cd) is the unit of luminous intensity in a given direction, defined
by taking the fixed numerical value of the luminous efficacy of monochromatic
radiation of frequency 540 × 10
12 Hz, K cd , at 683 when expressed in the unit
lm W
−1 , which is equal to cd sr W
−1 , or cd sr kg
−1 m
−2 s
3 , where the kilogram,
metre and second are defined in terms of h, c and Δν Cs .
Derived unit is a unit of measurement of the derived quantity in a given system of
quantities. Derived units in SI are linked to the base SI units, according to the physical
dependencies between quantities. The derived unit is, among others: the unit of area
in square meters (m
2 ); volume unit in cubic meters (m
3 ); and linear speed in meters
per second (m • s
−1 ). Some of them are given special names (Table 3.1).
SI units of measurement are recommended in all cases of international trade
and the regulations are adopted and accepted almost all over the world. However,
there are many units that do not belong to the international SI system, but they
1 The element Cs was named after the Latin word caesius, meaning bluish grey. Caesium is the
spelling recommended by the International Union of Pure and Applied Chemistry (IUPAC); the
American Chemical Society (ACS) has used the spelling cesium since 1921, following Webster’s
New International Dictionary.
27
units, which together with the derived units make up a coherent system of units of
measurement. In addition, certain entities outside of the system are accepted for use
with SI units.
The base units of the international system of units (SI):
• The second (s) is the unit of time, defined by fixed numerical value of the caesium
1
frequency Δν Cs , the unperturbed ground-state hyperfine transition frequency of
the caesium 133 atom, at 9,192,631,770 when expressed in the unit Hz, which is
equal to s
−1 .
• The meter (m) is the unit of length, defined by the fixed numerical value of the
speed of light in vacuum, c, at 299,792,458 when expressed in the unit m s
−1 ,
where the second is defined in terms of the caesium frequency Δν Cs .
• The kilogram (kg) is the unit of mass, defined by taking the fixed numerical value
of the Planck constant h to be 6.626070040 × 10
−34 when expressed in the unit
J s, which is equal to kg m
2 s
−1 , where the metre and the second are defined in
terms of c and Δν Cs
• The ampere (A) is the unit of electric current, defined by fixed numerical value
of the elementary charge e at 1.6021766208 × 10
−19 when expressed in the unit
C, which is equal to A s, where the second is in terms of Δν Cs .
• The kelvin (K) is the unit of the thermodynamic temperature, defined by taking
the fixed numerical value of the Boltzmann constant k at 1.38064852 × 10
−23
when expressed in the unit J K
−1 , which is equal to kg m
2 s
−1 K
−1 , where the
kilogram, metre and second are defined in terms of h, c and Δν Cs .
• The mole (mol) is the unit of amount of substance of a specific elementary entity,
which may be an atom, molecule, ion, electron or any other particle or a specified
group of such particles, defined by the fixed numerical value of the Avogadro
constant N A at 6.022408 s57 × 10
23 when expressed in the unit mol
−1 .
• The candela (cd) is the unit of luminous intensity in a given direction, defined
by taking the fixed numerical value of the luminous efficacy of monochromatic
radiation of frequency 540 × 10
12 Hz, K cd , at 683 when expressed in the unit
lm W
−1 , which is equal to cd sr W
−1 , or cd sr kg
−1 m
−2 s
3 , where the kilogram,
metre and second are defined in terms of h, c and Δν Cs .
Derived unit is a unit of measurement of the derived quantity in a given system of
quantities. Derived units in SI are linked to the base SI units, according to the physical
dependencies between quantities. The derived unit is, among others: the unit of area
in square meters (m
2 ); volume unit in cubic meters (m
3 ); and linear speed in meters
per second (m • s
−1 ). Some of them are given special names (Table 3.1).
SI units of measurement are recommended in all cases of international trade
and the regulations are adopted and accepted almost all over the world. However,
there are many units that do not belong to the international SI system, but they
1 The element Cs was named after the Latin word caesius, meaning bluish grey. Caesium is the
spelling recommended by the International Union of Pure and Applied Chemistry (IUPAC); the
American Chemical Society (ACS) has used the spelling cesium since 1921, following Webster’s
New International Dictionary.