Measurement of Length
Length can be measured using metre scale (10-3m to 102m), verniercallipers (10-4m) and screw gauge and spherometer (10-5m).
Range of Length
Size of object or distance |
Length (m) |
Size of proton |
10-15 |
Size of atomic nucleus |
10-14 |
Length of typical virus |
10-8 |
Wavelength of light |
10-7 |
Thickness of paper |
10-4 |
Height of Mount Everest above sea level |
104 |
Radius of earth |
107 |
Distance of moon from earth |
108 |
Distance of sun from earth |
1011 |
Distance of pluto from sun |
1013 |
Size of our galaxy |
1021 |
Distance to Andromeda Galaxy |
1022 |
Distance to observable universe boundaries |
1026 |
Measuring large Distances – Parallax Method
- Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines. Distance between the two viewpoints is called Basis.
Measuring distance of a planet using parallax method
Similarly, α = d/D
Whereα = angular size of the planet (angle subtended by d at earth) and d is the diameter of the planet.αis angle between the direction of the telescope when two diametrically opposite points of the planet are viewed.
Measuring very small distances
To measure distances as low as size of a molecule, electron microscopes are used. These contain electrons beams controlled by electric and magnetic fields.
- Electron microscopes have a resolution of 0.6 Å or Agstroms.
- Electron microscopes are able to resolve atoms and molecules while using tunneling microscopy, it is possible to estimate size of molecule.
Estimating size of molecule of Oleic acid
The steps followed in determining the size of molecule are:
- Dissolve 1 cm3 of oleic acid in alcohol to make a solution of 20 cm3.Take 1 cm3 of above solution and dissolve in alcohol to make a solution of 20 cm3 Concentration of oleic acid in the solution will be (1/(20×20)) cm3.
- Sprinkle lycopodium powder on the surface of water in a trough and put one drop of above solution. The oleic acid in the solution will spread over water in a circular molecular thick film.
- Measure the diameter of the above circular film using below calculations.
- If n –Number of drops of solution in water, V – Volume of each drop, t – Thickness of the film, A – Area of the film
Total volume of n drops of solution = nV cm3
Amount of Oleic acid in this solution = nV(1/(20×20)) cm3
Thickness of the film = t = Volume of the film / Area of the film
t = nV/(20x20A) cm