# Lesson Explainer: SI Unit Definitions Physics

In this explainer, we will learn how to recognize the units of the SI unit system and the physical quantities that it is used to measure.

The SI system of units is the international system of units. SI is abbreviated from the French “système international.” The SI system was established in 1960 and has become the standard system of units for scientists throughout most of the world.

The units of the SI system are each associated with a quantity. Probably the most immediately recognizable such quantities are named in the following list:

• length,
• time.

These are two of the quantities of the SI system that are known as base quantities.

A base quantity is a quantity that cannot be separated into more fundamental parts. A quantity that can be separated into more fundamental parts is known as a compound or derived quantity.

An example of a derived quantity is the quantity equal to

This quantity has the name “speed.” We see that it consists of the ratio of two base quantities.

Length and time consist only of themselves. It is of course true that because it must be the case that

This might make it seem that the base quantity “length” can be obtained from other quantities, but this is misleading, as one of these quantities is itself obtained from base quantities. The expression written in full is

A base quantity will necessarily be equal only to itself when any derived quantities that it is related to are expressed in terms of the base quantities that they are obtained from.

Base quantities are also known as fundamental quantities.

Let us look at an example that compares fundamental quantities.

### Example 1: Distinguishing between Fundamental and Derived Quantities

Which of the following most correctly describes the difference between fundamental and derived physical quantities?

1. Derived quantities can be defined in terms of fundamental quantities.
2. Fundamental quantities can be defined in terms of derived quantities.
3. Derived quantities can have more than one unit, but fundamental quantities can only have one unit.
4. Fundamental quantities can have more than one unit, but derived quantities can only have one unit.
5. Fundamental quantities were proposed before derived quantities were proposed.

### Answer

Time can be measured in seconds, minutes, hours, days, and years. Time is a fundamental quantity. It cannot then be true that fundamental quantities can only have one unit.

Speed can be measured in kilometres per hour and in miles per hour. Speed is a derived quantity. It cannot then be true that derived quantities can only have one unit.

Some fundamental quantities were proposed a very long time ago. The idea of length and time being measurable is so old that it is unknown when the idea first appeared. This means that there is no way to know with confidence whether the idea of measuring time or length is as old as, older than, or less old than the idea of measuring speed.

Fundamental and derived quantities can be expressed in terms of each other.

A derived quantity expressed in terms of fundamental quantities is

A fundamental quantity expressed in terms of a derived and a fundamental quantity is

However, speed is itself obtained from length and time, so expressing time in terms of speed is really expressing the following:

This is equivalent to which is equivalent to

We see then that it is most correct to say that derived units can be defined in terms of fundamental quantities. These are also called base quantities. This corresponds to option A.

The SI base unit of length is the metre.

The SI base unit of time is the second.

The length that is equal to one metre is defined by a measurement of a naturally occurring physical phenomenon.

The time that is equal to one second is defined by a measurement of a naturally occurring physical phenomenon.

Both these phenomena are related to the light emitted from atoms. This light consists of waves that have a particular length and that are generated in a particular time.

Another base SI quantity has a unit that is not defined by the measurement of a naturally occurring physical phenomenon but rather by an artificially produced object. No other SI base quantity is defined in this way. The quantity that has this unique method of definition is the quantity mass.

In the interests of accuracy, it must be mentioned that the definition of the base unit of mass in the SI system has now been changed so as not to rely on a specific object. This change is recent, however, and the new definition is sufficiently complex to explain that it is preferable to continue to refer to the older definition that is based on a specific object.

The SI base unit of mass is the kilogram. Perhaps surprisingly, the kilogram rather than the gram is the base unit of mass. This is different to the case for length and time. The SI base unit of length is not the kilometre and the SI base unit of time is not the kilosecond.

The kilogram was originally defined as the mass of a litre of water. In the year 1889, however, a very specifically designed object was made. This object was a cylinder made of platinum–iridium alloy. After this object was made, a kilogram was defined as being equal to the mass of this object. This object is referred to as the prototype kilogram.

The prototype kilogram exists purely to define the mass that is equal to 1 kilogram. The shape of the prototype kilogram and the substance of which it is made are not essential features of the prototype kilogram. Different shapes and substances could have been chosen. The only property of the prototype kilogram that is relevant is its mass.

Let us look at an example involving an SI base unit definition.

### Example 2: Defining an SI Base Unit

Which of the following SI units is defined as being equal to 1‎ ‎650‎ ‎763.73 wavelengths of the red-orange light emitted in a vacuum by atoms of krypton-86?

1. The metre
2. The second
3. The mole
4. The candela
5. The steradian

### Answer

To determine the SI unit defined in the question, it is helpful to determine which SI quantity the definition refers to a measurement of.

Most of the information given in the definition has no direct relevance to determining which quantity is measured. The value 1‎ ‎659‎ ‎763.73 could be the value of any quantity. The element the definition refers to an atom of does not uniquely identify any quantity.

The definition mentions light emitted by an atom. From this, it might be thought that the quantity involved is something to do with light and that this perhaps means that the unit defined is the candela, which has a name that suggests a connection to light.

Reading the definition carefully, however, we notice that the name of a quantity is mentioned in the definition as follows: “1‎ ‎650‎ ‎763.73wavelengths of the red-orange light emitted in a vacuum by atoms of krypton-86.”

This is a definition of a length that is equal to the SI base unit of length, which is the metre. This corresponds to option A.

Let us look at another example involving an SI base unit definition.

### Example 3: Defining an SI Base Unit

Which of the following SI units is defined as being equal to the interval in which atoms of cesium-133 emit 9‎ ‎192‎ ‎631‎ ‎700 waves?

1. The second
2. The metre
3. The mole
4. The candela
5. The steradian

### Answer

To determine the SI unit defined in the question, it is helpful to determine which SI quantity the definition refers to a measurement of.

Most of the information given in the definition has no direct relevance to determining which quantity is measured. The value 9‎ ‎192‎ ‎631‎ ‎700 could be the value of any quantity. The element the definition refers to an atom of does not uniquely identify any quantity.

The definition mentions waves emitted by an atom. From this, it might be thought that the quantity involved is something to do with wavelength and that this perhaps means that the quantity involved is length.

Reading the definition carefully, however, we notice that it mentions an interval as follows: “the interval in which atoms of cesium-133 emit 9‎ ‎192‎ ‎631‎ ‎700 waves.”

In other words, it is an interval in which atoms of cesium-133 emit a wave 9‎ ‎192‎ ‎631‎ ‎700 times.

This way of expressing the statement clarifies that it refers to an interval of time and so refers to the quantity time. The SI base unit of time is the second. This corresponds to option A.

Let us look at another example involving an SI base unit definition.

### Example 4: Defining an SI Base Unit

Which of the following SI units is defined by reference to the properties of a unique, standard object held at the International Bureau of Weights and Measures?

1. The kilogram
2. The metre
3. The mole
4. The candela
5. The steradian

### Answer

Only one SI base unit is defined by a specific object. The standard kilogram mass is an object that has a mass that defines the mass equal to a kilogram.

It might be supposed that a specific object with a length that defines one metre might also exist, but actually the metre is defined in terms of a naturally occurring phenomenon.

The correct option is A.

We have seen so far three SI base quantities and their units.

QuantitySI Base UnitUnit Symbol
LengthMeterm
TimeSeconds
MassKilogramkg

There is another SI base quantity that is called “amount of substance.” This name, though, does not make what is meant by “amount” entirely clear. The lack of clarity in this meaning can result in confusion between this quantity and the quantity of mass.

A more specific and detailed expression of the meaning of the quantity called “amount of substance” can be given. “Amount of substance” is the number of equivalent parts that an object that is made of a substance consists of.

The most commonly used equivalent parts that are counted in moles are atoms or molecules. Different atoms of the same element are for most purposes considered completely equivalent to each other.

In the SI system, the base unit of “mole” refers to a specific number of equivalent parts. This number is . One mole of a substance refers to an object containing this number of equivalent parts.

We can compare the number of moles of different amounts of different types of equivalent parts found in different objects as follows.

• As stated, atoms and molecules are the kinds of parts that are usually counted in moles, as atoms of the same element are equivalent for most purposes. For example, 4 grams of helium contain helium atoms. The number of helium atoms in 4 grams of helium equals the number of equivalent parts in a mole. There is therefore 1 mole of atoms in 4 grams of helium.
• We can use moles to count the number of other types of objects that are similar to each other, but not anywhere near as similar to each other as atoms are. For example, we could count the number of moles of tennis balls in an incredibly huge container of tennis balls. If this container held tennis balls, the number of moles of tennis balls in the container would be the number of tennis balls divided by the number of equivalent parts in a mole. This would be
• Let us now suppose that we consider objects that can differ from each other considerably more than tennis balls do. Stars can be very different from each other in many ways (such their size, temperature, and brightness). The Milky Way galaxy contains approximately stars. This is converted to a number of moles of stars by dividing the number of stars by the number of equivalent parts in a mole. This would be
• Suppose instead that the number of moles of humans in the human population of Earth is counted. Approximately humans live on Earth. This is converted to a number of moles of humans by dividing the number of stars by the number of equivalent parts in a mole. This would be

Obviously, people are not equivalent to each other, although in terms of physical quantities, humans are generally more similar to each other than stars are.

We would never normally use moles to count things like tennis balls. The above examples show that theoretically we could, but in practice this is not done.

In summary, the mole is the unit of measurement for amount of substance. A mole is defined as exactly particles, which may be atoms, molecules, ions, or electrons. In short, 1 mole equals parts.

Using moles to count different equivalent parts of objects is summarized in the following table.

ObjectEquivalent Parts of the ObjectNumber of Equivalent PartsNumber of Moles
4 grams of heliumAtoms
An incredibly huge container of tennis ballsTennis balls
The Milky Way galaxyStars
The human population of EarthHumans

It is important to remember that only atoms and molecules are usually counted in moles.

Based on what we have seen, then, a mole is defined as shown in the following table.

QuantitySI Base UnitUnit Symbol
Amount of substanceMolemol

Let us now look at an example concerning the mole.

### Example 5: Defining the Mole

Which of the following physical quantities has the SI unit mole?

1. Amount of substance
2. Mass
3. Volume
4. Density
5. Energy

### Answer

The mole defines a number of equivalent parts.

This might be supposed to refer to the mass of an object, but in fact the parts of an object can themselves have mass.

The parts of an object can also have a volume.

Density is the ratio of mass to volume, so this also cannot be the quantity that the mole is the base unit of.

The energy of something is not a measurement of the number of equivalent parts of that thing. Changing the energy of something does not mean changing the number of equivalent parts that it consists of.

The measurement of the number of equivalent parts of something is a measurement of the amount of substance. The mole is the SI base unit of this quantity. This corresponds to option A.

Another familiar SI base quantity is temperature. Temperature is a familiar quantity, but the SI base unit of temperature is not as familiar. The most familiar units of temperature are degrees Celsius and degrees Fahrenheit. Neither of these are the SI base unit of temperature.

The SI base unit of temperature is defined so that the minimum possible temperature equals zero of these units. Both Celsius and Fahrenheit scales have negative as well as positive values of temperature. The unit of temperature for which there are no negative temperature values is the unit of “kelvin.” A temperature measured in kelvin is called an absolute temperature.

Let us now look at an example concerning the kelvin.

### Example 6: Defining the SI Unit of Temperature

Which of the following is the symbol for the SI unit of absolute temperature?

1. K
2. C

### Answer

The unit of absolute temperature is the kelvin, so the question is asking what the symbol for the unit kelvin is.

The symbol for the unit degrees Celsius is and the symbol for the unit degrees Fahrenheit is . Neither of these units are units of absolute temperature.

The symbol is the symbol for the unit “degree,” which is not a unit of temperature but a unit of angular distance.

The unit symbol for the kelvin is therefore either C or K. It might be supposed that as the initial of the word kelvin is k, that the symbol for kelvin is K. This is in fact correct. The k is capitalized as the kelvin is named after a person, and all units that are named after people have capitalized symbols.

This correct option is A.

We can add the mole and the kelvin to the table of SI base quantities and units and add two more entries to the end of the table that we have not discussed in the explainer, but which do exist.

QuantitySI Base UnitUnit Symbol
LengthMeterm
TimeSeconds
MassKilogramkg
Amount of substanceMolemol
Absolute temperatureKelvinK
Electric currentAmpereA
Luminous intensityCandelacd

Looking at the last entry, we see that the candela, which was mentioned in an earlier example, is in fact associated with light, as the word luminous means relating to light.

Let us now summarize what has been learned in this explainer.

### Key Points

• The SI unit system is the standard system for making scientific measurements.
• A base quantity is a quantity that cannot be derived from other quantities.
• The SI base quantities are length, time, mass, amount of substance, absolute temperature, electric current, and luminous intensity.
• Each base quantity has a unit, and each unit has a unit symbol.
• A derived quantity is obtained by multiplying or dividing base quantities by each other.

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