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## Definition of Fundamental Units

The fundamental units are the base units defined by the International System of Units. These units are not derived from any other unit. Therefore they are called fundamental units.

The International System of Units (SI) is a system of units of measurement that is widely used worldwide. This modern form of the Metric system is based around the number 10 for convenience.

A set unit of prefixes have been established and are known as the SI prefixes or the metric prefixes (or units). The prefixes indicate whether the unit is a multiple or a fraction of the base ten. It allows the reduction of zeros of a very small number or a very larger number such as 0.000000001 meters and 7,500,000 Joules into 1 nanometer and 7.5 Megajoules, respectively.

These SI prefixes also have a set of symbols that precede unit symbols. However, countries such as the United States, Liberia, and Burma have not officially adopted the International System of Units as their primary system of measurements.

Since the SI Units are nearly globally though, the scientific and mathematical field will use these SI units to provide ease between the sharing data with one another because of a common set of measurements.

## Units of the SI System

There are seven base units in the SI system :

- The kilogram (kg), for mass.
- The second (s), for time.
- The kelvin (K), for temperature.
- The ampere (A), for electric current.
- The mole (mol), for the amount of a substance.
- The candela (cd), for luminous intensity.
- The meter (m), for distance.

## Base Fundamental Units

The SI contains seven BASE UNITS that each represent a different kind of physical quantity. These are commonly used as a convention

Physical Quantity | Name of Unit | Abbreviation |

Mass | Kilogram | Kg |

Length | Meter | m |

Time | Second | s |

Temprature | Kelvin | K |

Amount of Substance | Mole | mol |

Electric Current | Ampere | A |

Luminous Intensity | Candela | cd |

## History of the SI System

The SI units of measurement have an interesting history. Over time they have been refined for clarity and simplicity.

- The meter (m), or meter, was originally defined as 1/10,000,000 of the distance from the Earth’s equator to the North Pole measured on the circumference through Paris. In modern terms, it is defined as the distance travelled by light in a vacuum over a time interval of 1/299,792,458 a second.
- The kilogram (kg) was initially defined as the mass of a litre (i.e., one-thousandth of a cubic meter). It is currently defined as the mass of a platinum-iridium kilogram sample maintained by the Bureau International des Poids et Measures in Sevres, France.
- The second (s) was initially based on a “standard day” of 24 hours, with each hour divided into 60 minutes and each minute divided into 60 seconds. However, we now know that a complete rotation of the Earth takes 23 hours, 56 minutes, and 4.1 seconds. Therefore, a second is now defined as 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.
- The ampere (A) measures the amount of electric charge passing a point in an electric circuit per unit of time. 6.241×1018electrons, or one coulomb, per second, constitutes one ampere.
- The kelvin (K) is the unit of the thermodynamic temperature scale. This scale starts at 0 K. The total size of the kelvin is the same as that of the degree on the Celsius (also called centigrade) scale. The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water (precisely 0.01 °C, or 32.018 °F)
- The mole (mol) is a number that relates molecular or atomic mass to a constant number of particles. It is defined as the amount of a substance containing as many elementary entities as atoms in 0.012 kg of carbon-12.
- The candela (cd) was so named to refer to “candlepower” back in the days when candles were the most common source of illumination (because so many people used candles, their properties were standardized). With the prevalence of incandescent and fluorescent light sources. The candela is defined as the luminous intensity in a given direction of a source that emits monochromatic radiation of frequency 540⋅1012 Hertz, which has a radiant intensity in that direction of 1/683 watts per steradian.

## Basic Fundamental Units

### Kilogram

Kilogram (kg) is the fundamental unit of mass in the metric system. A kilogram is nearly equal (originally intended to be exactly equal) to the mass of 1,000 cubic cm of water. The pound is defined as equal to 0.45359237 kg, exactly.

- As originally defined, the kilogram was represented in the late 18th century by a solid cylinder of platinum. Measurements of the mass of a volume of water proved to be imprecise and inconvenient to make. However, and the platinum artefact itself became the standard.
- It was superseded in 1889 by a standard kilogram, a solid cylinder of height equal to its diameter, made of the same platinum-iridium alloy as the bar, then used as the standard for defining the meter. The standard kilogram was kept at the International Bureau of Weights and Measures laboratory at Sevres, France.
- However, in 1989 it was discovered that the prototype kept at Sevres was 50 micrograms lighter than other copies of the standard kilogram.
- To avoid the problem of having the kilogram defined by an object with a changing mass. The General Conference on Weights and Measures (CGPM) agreed in 2011 to a proposal to begin to redefine the kilogram not by a physical artefact but by a fundamental physical constant.
- The constant chosen was Planck’s constant, which was to be defined as equal to 6.62607015 × 10
^{-34}joule second. One joule is equal to one-kilogram times meter squared per second squared. Since the second and the meter were already defined in terms of the frequency of a spectral line of caesium and the speed of light. Respectively, the kilogram would then be determined by accurate measurements of Planck’s constant. - The proposal was accepted at the 2018 CGPM and, effective from May 20, 2019, the kilogram would be defined by Planck’s constant. See also International System of Units.

## Second

Second, fundamental unit of time, now defined in terms of the radiation frequency at which atoms of the element cesium change from one state to another.

- The second was formerly defined as 1/86,400 of the mean solar day—i.e., the average period of rotation of the Earth on its axis relative to the Sun.
- The mid-20th century, this definition became inadequate because of the need for increased precision in timekeeping. In 1956 the second was redefined by the International Committee on Weights and Measures as 1/31,556,925.9747 of the length of the tropical (seasonal) year 1900.
- In 1967 the 13th General Conference on Weights and Measures provisionally defined the second as 9,192,631,770 cycles of radiation associated with the transition between the two hyperfine levels of the ground state of the caesium-133 atom (see atomic time).
- The number of cycles of radiation was chosen to make the length of the defined second correspond as closely as possible to that of the now obsolete astronomically determined second of Ephemeris Time (defined as the fraction of the tropical year given above).
- As the Earth’s rate of rotation constantly changes, it is necessary to occasionally add (or theoretically to subtract) a second during the year to ensure the atomic timescale Coordinated Universal Time (UTC) stays in synchronization with nature. This represents the sole definition of the second in the International System of Units (SI).

### Kelvin

Kelvin (K) is the base unit of thermodynamic temperature measurement in the International System of Units (SI).

- The 2018 General Conference on Weights and Measures decided that effective from May 20, 2019; the unit would be defined such that the Boltzmann constant would be equal to 1.380649 × 10
^{-23}joule per kelvin. - This unit was initially defined as 100/27,316 of pure water’s triple point (equilibrium among the solid, liquid, and gaseous phases). The kelvin is also the fundamental unit of the Kelvin scale, an absolute temperature scale named for the British physicist William Thomson (known as Lord Kelvin).
- An absolute temperature scale has as it’s zero points absolute zero (−273.15° on the Celsius temperature scale and −459.67° on the Fahrenheit temperature scale), the theoretical temperature at which the molecules of a substance have the lowest energy; hence, all values on such a scale are non-negative.
- Many physical laws and formulas can be expressed more simply when an absolute temperature scale is used; accordingly, the Kelvin scale has been adopted as the international standard for scientific temperature measurement.
- The difference between the freezing and boiling point of water is 100 degrees in both the Kelvin and Celsius scales. Thus, the Kelvin degree has the same magnitude as the Celsius degree.

### Ampere

Ampere, unit of electric current in the International System of Units (SI), used by both scientists and technologists.

- In 2018 the General Conference on Weights and Measures (CGPM) agreed that on May 20, 2019, the ampere would henceforth be defined such that the elementary charge would be equal to 1.602176634 × 10
^{-19}coulomb. - Earlier the ampere was defined as the constant current which, if maintained in two straight parallel conductors of the infinite length of negligible circular cross-section and placed one meter apart in a vacuum, would produce between these conductors a force equal to 2 × 10
^{-7}newton per meter of length. - Named for 19th-century French physicist André-Marie Ampère, it represents a flow of one coulomb of electricity per second. A flow of one ampere is produced in a resistance of one ohm by a potential difference of one volt.

### Mole

Mole, also spelt mol, in chemistry, is a standard scientific unit for measuring large quantities of very small entities such as atoms, molecules, or other specified particles

- The mole designates an extremely large number of units, 6.02214076 × 10
^{23}. - The General Conference on Weights and Measures defined the mole as this number for the International System of Units (SI) effective from May 20, 2019.
- The mole was previously defined as the number of atoms determined experimentally to be found in 12 grams of carbon-12. The number of units in a mole also bears the name Avogadro’s number, or Avogadro’s constant, in honour of the Italian physicist Amedeo Avogadro (1776–1856). Avogadro proposed that equal volumes of gases under the same conditions contain the same number of molecules, a hypothesis that proved useful in determining atomic and molecular weights and which led to the concept of the mole. The number of atoms or other particles in a mole is the same for all substances.
- The mole is related to the mass of an element in the following way: one mole of carbon-12 atoms has 6.02214076 × 10
^{23}atoms and a mass of 12 grams. - In comparison, one mole of oxygen consists, by definition, of the same number of atoms as carbon-12, but it has a mass of 15.999 grams. Oxygen, therefore, has a greater mass than carbon. This reasoning also can be applied to molecular or formula weights. The mole concept helps to put quantitative information about what happens in a chemical equation on a macroscopic level.

**For example**, in the chemical reaction 2H_{2}O → O_{2} + 2H_{2}, two moles of water are decomposed into two moles of molecular hydrogen and one mole of molecular oxygen. The mole can determine the simplest formula of a compound and calculate the quantities involved in chemical reactions. When dealing with reactions that take place in solutions, the related concept of molarity is useful. Molarity (M) is defined as the number of moles of a solute in a litre of solution.

### Candela

Candela (cd), unit of luminous intensity in the International System of Units (SI), is defined as the luminous intensity in a given direction of a source that emits monochromatic radiation of frequency 540 ×10^{12} hertz and has a radiant intensity in that same direction of 1/683 watt per steradian (unit solid angle).

- The candela has replaced the standard candle or lamp as a unit of luminous intensity in calculations involving artificial lighting and is sometimes called the “new candle.”

### Meter

Meter (m), also spelled meter, in measurement, fundamental unit of length in the metric system and in the International Systems of Units (SI).

- It is equal to approximately 39.37 inches in the British Imperial and United States Customary systems.
- The French Academy of Sciences historically defined the meter in 1791 as 1/10,000,000 of the quadrant of the Earth’s circumference running from the North Pole through Paris to the equator.
- The International Bureau of Weights and Measures in 1889 established the international prototype meter as the distance between two lines on a standard bar of 90 percent platinum and 10 percent iridium.
- By 1960 advances in the techniques of measuring light waves had made it possible to establish an accurate and easily reproducible standard independent of any physical artefact. In 1960 the meter was thus defined in the SI system as equal to 1,650,763.73 wavelengths of the orange-red line in the spectrum of the krypton-86 atom in a vacuum.

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