# Units and Measurement

## Measurement

Comparison of a physical quantity with certain basic, arbitrarily chosen internationally accepted reference standard (called unit) is called measurement. The result of a measurement of a physical quantity is expressed by a number accompanied by a unit.

## Fundamental Unit

The units for the fundamental or base quantities are called fundamental or base units. Units of all other physical quantities can be expressed as combinations of the base units. Such units for the derived quantities are called derived units. A complete set of these units is called the system of units.

SI Units | |||
---|---|---|---|

Base quantity | Name | Symbol | Definition |

Length | meter | m | Metre is the length of path travelled by light in vacuum during a time interval of 1/299,792,458 of a second. |

Mass | kilogram | kg | Kilogram is equal to the mass of the international prototype of the kilogram (a platinum-iridium alloy cylinder) kept at international Bureau of Weights and Measures, at Sevres, near Paris, France. |

Time | second | s | 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 cesium-133 atom. |

Electric current | ampere | A | The constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum would produce between these conductors a force equal to 10 × 10^{-7} newton per meter of length. |

Thermodynamic temperature | kelvin | K | The fraction 1/273.16 of the thermodynamic temperature of the triple point of water. |

Amount of substance | mole | mol | The amount of substance of a system, which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon – 12. |

Luminous intensity | candela | cd | Luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 10^{12} hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. |

## Parallax Method:

Let us assume that we need to measure the distance D of a far away planet S by parallax method. We observe the planet from two different positions A and B on the earth. Let us assume that these positions are separated by distance AB = b. The angle between two directions (along which the planet is viewed) is measured. In the given figure ∠ASB = θ is called the parallax angle or parallactic angle.

As the planet is very far away, so `b/D`<< 1

Therefore, θ is very small

Now, take AB as an arc of length b of a circle with centre at S and distance D as radius AS = BS

So, AB = b = D θ

Where θ is in radians

`D=b/θ` ……………..(1)

After determining D, we can use this method to find the size or angular diameter of the planet. If d is the diameter of the planet and α is the angular size of the planet (the angle subtended by d at the earth), we have

`α=d/D` ………….(2)

Here, angle α can be measured from the same location on the earth. It is the angle between two directions when two diametrically opposite points of the planet are viewed through the telescope.

### Estimation of very small size

Molecular Size of Oleic Acid: Oleic acid is a soapy liquid with large molecule size of 10^{-9} m. For this, 1 cm^{2} of oleic acid is dissolved in alcohol to make a solution of 20 cm^{3}. After that, 1 cm^{3} of this solution is taken and diluted to 20 cm^{3}. Now, that concentration of the solution becomes `1/(20×20)` cm^{3} of oleic acid per cm^{3} of solution.

Then, some lycopodium powder is lightly sprinkled on the surface of water in a large trough; followed by putting one drop of this solution in water. Oleic acid drop spreads into a thin, large and roughly circular film of molecular thickness on water surface.

Diameter of the thin film is quickly measured and area A of this film is calculated.

If n drops are put in water then approximate volume of each drop can be determined as follows:

Volume of n drops of solution = nV cm^{3}

Amount of oleic acid in this solution

`=nV(1/(20×20))` cm^{3}

If the area of thin film is A cm^{2}, the thickness of the film

t = Volume of film ÷ Area of film

Or, `t=(nV)/(20×20A)` cm ………….(3)

Let us assume that the film has mon-molecular thickness, then it becomes the size of diameter of a molecule of oleic acid. The value of this is of the order of 10^{-9} m.