Measurement of very small distances | Using Avogadro’s Hypothesis

Measurement of very small distances

1.  Very small distance like size of molecules, radius of atoms etc, cannot be measured with the help of instruments like vernier calliperse, screw gauge, spherometer etc. Even optical microscope cannot measure these distances. In optical microscopes cannot measure these distances. In optical microscopes, visible light is used whose wavelength is of the order of 6 × 10^-7 m. Hence, we cannot see as object by an optical microscope whose dimension is less than 6 × 10^-7 m. Light will pass through such object instead of being scattered.

Measurement of very small distances

1. Electron microscope is a device which can measure distance of the order of 10-8m. In this microscope, we use an accelerated beam of electrons instead of visible light while focusing is done with the help of electric and magnetic fields. Electron microscope heaving resolution of A, can resolve atoms and molecules in a material.
2. Distance between molecules of crystals can be measured by x-ray diffraction experiments. Subatomic distances can be measured by alpha particle scattering experiments.
3. These are also some indirect methods for the measurement of microscopic distances. These methods may be used if only a rough estimate of small distances id desired. Two such methods are described below.
4. a) Using Avogadro’s Hypothesis: Because the atoms are spherical in shape, hence when a large number of atoms are put together, the vacant spaces are left between them and the actual volume occupied by the atoms in a substance is always less than the volume of that substance. According to Avogadro’s hypothesis, “the actual volume occupied by the atoms in a certain mass of a substance is two-thirds the volume occupied by that mass of the substance”.


5. Consider a monoatomic substance having mass m and volume V. If M and N are molecular weight of the substance and Avagadro’s number respectively, the number of atoms of the substance having mass m= N/M meter
   Assuming that each atom is a sphere of radious r, the volume occupied by atoms in the substance.
   V’ = (mN/M ) × (4/3)πr³
   Because, according to Avogadro’s hypothesis, all the atoms in a given specimen of the substance occupy 2/3 rd the volume V of the substance, hence
   (4/3)πr³ X mN/M=(2/3)V=(2/3)m/ρ  (ρ = density of substance)
   Or   r=(M/2πN ρ)^1/3
   Thus, knowing the values of M, N and ρ, r can be calculated.


6. b) Molecular layer method:  It is a practical method for estimating the size of the molecule of a liquid. The basic idea behind this method is to prepare a layer of one molecule thickness of a liquid on water. This method is quite adequate for the liquids whose molecules are quite big in size. Oleic acid is a very good example of such liquid.



Measurement of very small distances



7. First of all, a solution of known concentration of oleic is prepared. Suppose 1 c.c of oleic acid is dissolved in 500 c.c. alcohol, to prepare a solution of 1/500 concentration. Now pour a few drops of this solution on the surface of water in a flat dish. The film of solution so formed is stretched carefully as much as possible, so that its thickness is just equal to molecular size. After sometime, the alcohol will evaporate leaving behind a film of oleic acid on water. Let A be the area of the film, which is carefully measured using a tracing paper and graph paper.
   If V is the volume of one drop, then the volume of n drops of solution =nV
   Volume of oleic acid in n drops of solution =(nV)/500 c.c
   If A cm² is the surface area of the film and t cm its thickness, then we have
   A X t = nV/500  or t=nV/500A
   If the film of oleic acid is stretched to one molecule thickness, then the thickness of oleic acid film calculated above gives approximately the size of the molecule.