The International System of Units – Units, Rule & Advantages

The International System of Units (SI system) Is the collection of seven physical quantities that serve as the foundation for all other physical measurements. It is abbreviated as SI from the French name Le Syste ́me International d’Unite ́s. x

The SI units can be stated as fractional numbers or as standard multiples. These quantities are defined with the help of prefix multipliers with powers of 10 ranging from \(10^{-24}\) to \(10^{24}\). In the SI units system, the following are the seven quantities and their corresponding units: Mass, Length, Time, Temperature, Electric Current, Thermodynamic temperature, Amount of Substance, Luminous Intensity. 

What is International System of Units?

The International System of Units gives us units to measure the physical quantities accepted internationally. Before getting into the concept of The International System of Units, let us understand what physical quantities are and what units are.
Physical quantities: Physical quantities are the quantities that can be defined and measured—for example, Mass, Density, Force, Pressure, Work, etc.

The physical quantities are of two types – Fundamental Quantities and Derived Quantities.
Fundamental Quantities are the physical quantities that do not depend on any other physical quantity for their measurement. Mass, Length, Time, Electric Current, Temperature, Luminous Intensity and Amount of Substance are the Fundamental Quantities.
Derived Quantities are the physical quantities that are derived from the Fundamental Quantities. Density, Pressure, Velocity, Volume, Work, etc., are some of the Derived Quantities.
The measurement of a physical quantity consists of the magnitude and the unit. For example, the mass of an apple is written as \(150\,\rm{gram}\). Here \(150\) is the magnitude, and gram is the unit. Let us now understand what a unit is.
Units: A physical quantity is measured by comparing it with some standard quantity. This standard quantity used to measure the unknown quantity of a physical quantity is known as a unit.

There are many systems of units in use. Some of them are as under:

1. CGS System: In this system of units, length is measured in centimetres, mass is measured in grams and time is measured in second.
2. FPS System: In this system of units, length is measured in the foot, mass is measured in pounds and time is measured in second.
3. MKS System: In this system of units, length is measured in metres, mass is measured in kilograms and time is measured in seconds.
4. SI System: This is the internationally approved and extended version of the MKS system of units.

Thus, the SI system or The International System of Units is one among the various system of units that are in common use. Let us study The International System of Units in detail.

Importance of International System of Units

The International System of Units or SI is well explained in the SI brochure. The SI brochure is published by the Bureau International des Poids et Mesures, the BIPM (known in English as the International Bureau of Weights and Measures) to promote and explain SI. According to the SI brochure, SI was established in 1960 by a resolution at the \(11^{th}\) meeting of the Conférence Générale des Poids et Mesures, the CGPM (known in English as the General Conference on Weights and Measures).

The International System of Units is well used today in Sciences, Technology, Trade, Industry and other such fields. But in olden times, there were many such systems of units. The interconversion of these units for international exchanges, whether it’s the Science and Technology or the Trade and Industry or any other field, was indeed a challenge.

Looking into the complexities, the international community came together and adopted the modern form of the MKS system or the metric system and named it “The International System of Units” or “SI” for the smooth operation of various international activities across the globe, thereby ensuring worldwide uniformity in units of measurement. The International System of Units undergoes revision from time to time to incorporate scientific and technological developments to keep it updated.

The International System of Units Definition

The International System of Units consists of seven base quantities using which all the other quantities can be derived with the help of mathematical operators. They are defined, keeping in mind their invariability and availability. The definition of the seven base SI units are as under:

1. The SI unit of length is metre. It is symbolically written as m. It is defined by taking the fixed numerical value of the speed of light in vacuum \(c\), to be \(299792458\) when expressed in the unit \(\text{m s}^{−1}\), where the second is defined in terms of the caesium frequency \(∆ν_{Cs}\). It is the distance travelled by light in a vacuum during the time interval with duration \(\frac{1}{ {299792458}}\) second.
   \(\therefore 1\,{\text{m}} = \frac{c}{{299792458}} = \frac{{9192631770}}{{299792458\,{\text{∆ }}{v_{Cs}}}} \approx 30.663319\frac{c}{{{\text{∆ }}{v_{Cs}}}}\)
2. The SI unit of Mass is kilogram. It is symbolically written as kg. It is defined by taking the fixed numerical value of the Planck constant, \(h\), to be \(6.62607015 \times 10^{−34}\) when expressed in the unit \(\text{J s}\), which is equal to \(\rm{kg}\,\rm{m}^2\,\rm{s}^{−1}\), where the metre and the second are defined in terms of \(c\) and \(∆ν_{Cs}\). This is to define the unit of mass using the definitions of second and metre in terms of Planck constant \(h\). This is equal to the mass of the international standard prototype with a relative standard uncertainty of \(1 \times 10^{-8}\) which was the standard uncertainty of the combined best estimates of the value of the Planck constant at that time.
   \(1\,{\text{kg}} = \frac{h}{{6.62607015 \times {{10}^{ – 34}}{{\text{m}}^2}{{\text{s}}^{ – 1}}}}\)
   But that is equal to
   \(\therefore 1\,{\text{kg}} = \frac{{{{(299792458)}^2}}}{{\left({6.62607015 \times {{10}^{ – 34}}} \right)(9192631770)}}\frac{{h{\text{∆ }}{v_{Cs}}}}{{{c^2}}} \approx 1.4755214 \times {10^{40}}\frac{{h{\text{∆ }}{v_{Cs}}}}{{{c^2}}}\)
3. The SI unit of Time is second. It is symbolically written as \(s\). It is defined by taking the fixed numerical value of the caesium frequency, \(∆ν_{Cs}\), the unperturbed ground-state hyperfine transition frequency of the caesium \(133\) atom, to be \(9192631770\) when expressed in the unit \(\rm{Hz}\), which is equal to \(\rm{s}^{−1}\). So, one second is equal to the duration of \(9192631770\) periods of the radiation corresponding to the transition between the two hyperfine levels of the unperturbed ground state of the caesium \(133\) atom.
   \(\therefore 1\,{\text{s}} = \frac{{9192631770}}{{{\text{∆ }}{v_{Cs}}}}\)
4. The SI unit of Electric Current is ampere. It is symbolically written as \(\rm{A}\). It is defined by taking the fixed numerical value of the elementary charge, \(e\), to be \(1.602176634 \times 10^{−19}\) when expressed in the unit \(C\), which is equal to \(\text{A s}\), where the second is defined in terms of \(∆ν_{Cs}\). So, one ampere is the Electric Current corresponding to the flow of \(\frac{1}{ {1.602176634 \times { {10}^ { – 19}}}}\) elementary charges per second.
   \(1\,{\text{A}} = \frac{e}{{1.602176634 \times {{10}^{ – 19}}}}\,{{\text{s}}^{ – 1}}\)
   But that is equal to
   \(\therefore 1\,{\text{A}} = \frac{1}{{(9192631770)\left({1.602176634 \times {{10}^{ – 19}}} \right)}}{\text{∆ }}{v_{Cs}}e \approx 6.7896868 \times {10^8}{\text{∆ }}{v_{Cs}}e\)
5. The SI unit of Temperature is kelvin. It is symbolically written as \(\rm{K}\). It is defined by taking the fixed numerical value of the Boltzmann constant, \(k\) to be \(1.380649 \times 10^{−23}\) when expressed in the unit \(\text{J K}^{−1}\), which is equal to \(\text{kg m}^2 \text{s}^{−2} \text{K}^{−1}\), where the kilogram, metre and second are defined in terms of \(h, c\) and \(∆ν_{Cs}\). One kelvin is equal to the change of thermodynamic temperature that results in a change of thermal energy \(kT\) by \(1.380649 \times 10^{−23}\,\rm{J}.\)
   \(1\,{\text{K}} = \frac{{1.380649 \times {{10}^{ – 23}}}}{k}{\text{kg}}\,{{\text{m}}^2}{{\text{s}}^{ – 2}}\)
   But that is equal to
   \(\therefore 1\,{\text{K}} = \frac{{1.380649 \times {{10}^{ – 23}}}}{{\left({6.62607015 \times {{10}^{ – 34}}} \right)(9192631770)}}\frac{{{\text{∆ }}{v_{Cs}}h}}{k} \approx 2.2666653\frac{{{\text{∆ }}{v_{Cs}}h}}{k}\)
6. The SI unit of Amount of Substance is mole. It is symbolically written as \(\rm{mol}\). One mole contains exactly \(6.02214076 \times 10^{23}\) elementary entities. This number is the fixed numerical value of the Avogadro constant, \(N_A\), when expressed in the \(\rm{mol}^{−1}\) and is called the Avogadro number. So, one mole is the Amount of Substance of a system that contains \(6.02214076 \times 10^{23}\) specified elementary entities.
   \(\therefore 1\, {\text{mol}} = \frac{ {6.02214076 \times { {10}^ {23}}}}{ { {N_A}}}\)
7. The SI unit of Luminous Intensity is candela. It is symbolically written as \(\rm{cd}\). It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency \(540 \times 10^{12}\,\rm{Hz}\), \(K_{cd}\), to be \(683\) when expressed in the unit \(\text{lm W}^{−1}\), which is equal to \(\text{cd sr W}^{−1}\), or \(\text{cd sr kg}^{−1} \text{m}^{−2} \text{s}^3\), where the kilogram, metre and second are defined in terms of \(h, c\) and \(∆ν_{Cs}\). So, one candela is the Luminous Intensity, in a given direction, of a source that emits monochromatic radiation of frequency \(540 \times 10^{12} \text{Hz}\) and has a radiant intensity in that direction of \(\frac{1}{{683}}{\text{W}}\,{\text{s}}{{\text{r}}^{ – 1}}\)
   \(1\,{\text{cd}} = \frac{{{K_{cd}}}}{{683}}{\text{kg}}\,{{\text{m}}^2}{{\text{s}}^{ – 3}}{\text{s}}{{\text{r}}^{ – 1}}\)
   But that is equal to
   \(\therefore 1\,{\text{cd}} = \frac{1}{{\left({6.62607015 \times {{10}^{ – 34}}} \right){{(9192631770)}^2}683}}{\left({{\text{∆ }}{v_{Cs}}} \right)^2}h{K_{cd}}\)
   \(1\,{\text{cd}} \approx 2.6148305 \times {10^{10}}{\left({{\text{∆ }}{v_{Cs}}} \right)^2}h{K_{cd}}\)

Rules for Writing the International System of Units

The International System of Units has specific symbols that are written in a specific way. The general principles for writing the SI symbols are as under:

1. The symbol for a unit or the first letter of the symbol for a unit that is named after a scientist should start with an upper case letter. For example, pascal is written as \(\rm{Pa}\), newton is written as \(\rm{N}\), a joule is written as \(\rm{J}\), etc.
2. The symbol for a unit that is not named after a scientist is written in lower case letter. For example, a metre is written as \(\rm{m}\), a second is written as \(\rm{s}\), a mole is written as \(\rm{mol}\), etc.
3. In their full form, the units should start with a lower case letter—for example, joule, pascal, metre, second, etc.
4. The symbol of a unit should not be written in plural form. For example, we may write \(100\) metres as \(100\,\rm{m}\), \(40\) seconds as \(40\,\rm{s}\), etc.
5. A compound unit that is obtained from units of two or more physical quantities is written either by putting a dot or leaving a space between symbols of two units. For example, the unit of momentum is written as \(\text{N s}\) or as \(\text{N.s}\)
6. The denominator in a compound unit is written with negative power. For example, we write the unit of speed as \(\text{m s}^{-1}\).

Advantages of International System of Units

The International System of Units has a lot of advantages. Some of them are as mentioned below:

1. The International System of Units is internationally accepted. So, while coming across measurements to be presented internationally or even nationally, there will be uniformity and will not need further conversions.
2. Each physical quantity in The International System of Units has just one unit. This makes it easier to express the measurement of a physical quantity without having to choose among the other units of measurement available for a physical quantity.
3. The derived quantities are arrived at just by applying some simple mathematical operations. So, their interconversions become easier and simple.
4. The way The International System of Units is written makes the presentation simple and without any fraction or mathematical operations.
5. The usage of prefixes in The International System of Units makes its usage more user-friendly and thereby limits the number of units in the system.

Summary

We hope this article provides you with an insight into the International System of Units, including its base units and derived units. Here, you will also learn the advantages and rules of writing the International System of Units. Also, through this article, you will know how to use the International System of Units and why this system is better to use over the other systems.

FAQs

Q.1. What is a unit?
Ans: Unit is the standard quantity used to measure a physical quantity.

Q.2. What is the International System of Units?
Ans: The International System of Units is the modern version of the metric system that uses metre as the unit of length, the kilogram as the unit of mass and second as the unit of time.

Q.3. What is the other available system of units?
Ans: The other available system of units are the MKS system, FPS System and CGS system.

Q.4. What are the seven fundamental units in The International System of Units?
Ans: The seven fundamental units in The International System of Units are metre, kilogram, second, ampere, kelvin, mole and candela.

Q.5. What are the seven fundamental physical quantities in The International System of Units?
Ans: The seven fundamental physical quantities in The International System of Units are Length, Mass, Time, Electric Current, Temperature, amount of Substance and Luminous Intensity.

We hope this detailed article on The International System of Units helps you in your preparation. If you get stuck do let us know in the comments section below and we will get back to you at the earliest.