Range and Order of Lengths

The sizes of the objects in the universe varies in a wide range.

Size of a proton	10-15
Size of atomic nucleus	10-14
Size of hydrogen atom	10-10
Length of typical virus	10-8
Wavelength of light	10-7
Size of RBC	10-5
Thickness of a paper	10-4
Height of the Mt. Everest above sea level	104
Radius of the Earth	107
Distance of moon from the earth	108
Distance of the Sun from the earth	1011
Distance of Pluto from the Sun	1013
Size of our galaxy	1021
Distance to Andromeda galaxy	1022
Distance to the boundary of observable universe	1026

There are also some special units for large and small lengths

1 fermi = 1 f = 10^-15 m

1 angstrom = 1 Å = 10^-10 m

1 astronomical unit = 1 AU (average distance of the Sun from the Earth) = 1.496 × 10¹¹ m

1 light year = 1 ly = 9.46 × 10¹⁵ m (distance that light travels at 3 × 10⁸ m/s in a year)

1 parsec = 3.08 × 10¹⁶ m (distance at which average radius of earth's orbit subtends an angle of 1 arc second)

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Measurement of Length

For measuring large distances, parallax method is used

Parallax is an apparent displacement of an object viewed along two different lines of sight.

If we hold a pencil such that it covers a spot on the wall when our left eye is closed, and then open the left eye and close the right, parallax can be observed.

The distance between the two points of observation is called basis.

If we observe a planet S at a distance D from earth, from two points A and B which are d distance apart on earth, then, angle inscribed by AB on the planet, angle ASB is called parallax angle or parallactic angle. Here, we take AB as an arc of the circle with centre S and radius D.
So, D=b/angle ASB (if angle ASB is taken in radians). Thus we get D. (basis/angle)

Similarly, we can determine the diameter of the planet. If d is the diameter, and dAd' the angular size (angle subtended by d at earth),
then dAd' = d/D (diameter / distance)

For estimation of very small distances:we will have to use special methods.

An optical microscope can view objects of size greater than its wavelegth (4000 Å to 7000 Å) 1 angstrom = 1.0 × 10^-10 meters.

For smaller wavelengths, electron beams are used (electron micrsoscope). But due to the wave behaviour of electrons even this method has limitations. The maximum resolution of electron microscope is upto 0.6 Å.

Tuunneling microscopy is being developed which can go to even smaller scales.

But, the size of molecules can be estimated.

Oleic acid is a soapy liquid with a large molecular size.

1. 1 cu.cm of oelic acid is dissolved in alcohol to get 20 cu.cm solution.
2. 1 cu.cm of this solution is taken and diluted to 20 cu.cm using alcohol
   Now, the concentration of the solution is 1/400 cu.cm of oelic acid per cu.cm
3. some lycopodium powder is sprinkled on surface of water in a large trough
4. one drop of this solution is put in the water
   the oelic acid drop spreads into a thin, large, circular film of molecular thickness
5. The diameter of the film is measured to get its area.
6. The volume of the amount of drops we've put is determined.
   Let that be n cu.cm
7. The amount of oelic acid in this solution is
   n/400 cu.cm
8. The oelic acid forms a thin layer of thickness t
   this t = volume of the film/area of the film
   ie t = n / (400 * area ) cm
9. if the film is of mono-molecular thickness, then this becomes the diameter of oelic acid molecule.
   

Next: Range and Order of Lengths
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The Characteristics of a Good Unit

A good unit:

1. Must be internationally accepted
   
2. Must be well-defined
   
3. Must not vary with physical conditions, place or time
   
4. Must be of a size not too large or too small compared to the physical quantity that is to be measured
   
5. Must be accurate
   
6. Must be easily accessible
   
7. Must be easily reproducible
   
8. The conversions within a system of units must be simple and convenient

Next: Measurement of Length
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The International System of Units

Earlier, different countries were using different systems of measurement like CGS, FPS (or British) and MKS system

• CGS: centimetre, gram, second
  
• FPS: foot, pound, second
  
• MKS: metre, kilogram, second
  

Now, there is an internationally accepted system of measurements known as Systeme Internationale d' Unites (French for International System of Units) abbreviated as SI. It was developed by General Conference on Weights and Measures in 1971 for international usage.

Length	metre	m	Distance travelled by light in vacuum during 1/299,792,458 second
Mass	kilogram	kg	Mass of international prototype of kilogram at international Bureau of Weights and Measures
Time	second	s	duration of 9,192,631,770 periods of radiation corresponding to the transition between the two hyperfine levels of the ground state of cesium-133 atom
Electric current	ampere	A	that constant current which if maintained between two straight parallel conductors of infinite length, placed 1 metre apart in vacuum would produce a force 2 × 10–7 newton per metre of length
Thermodynamic temperature	Kelvin	K	1/273.16 of the thermodynamic temperature of the triple point of water
Amount of substance	mole	mol	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 × 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian

When mole is used elementary entities must be specified.

Next: The Characteristics of a Good Unit

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Units and Measurement

Physical Quantity: Anything that can be measured directly or indirectly.

Fundamental or Base Quantities: Basic non-derivable quantities (length, mass, time, electric current, thermodynamic temperature, amount of substance and luminous intensity)

Derived quantities: Quantities which are obtained from one or more fundamental quantities eg: velocity, acceleration

Supplementary Quantities: eg: solid angle, plane angle

Unit is the reference standard used to measure physical quantity.

Fundamental units: The reference standard used to measure fundamental physical quantities. (metre (m), kilogram (kg), second (s), ampere (A), Kelvin (K), mole (mol), candela(cd))

Derived units: The reference standard used to measure derived physical quantities. Eg newton, pascal, m/s

Supplementary units: The reference standard used to measure supplementary physical quantities. (for plane angles, radian, for solid angle – steradian) radian=length of arc/radius, steradian = intercepted area of sphere/radius

Next: The International System of Units

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