Give a method to measure size …
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Posted by Lochan Soni 6 years, 10 months ago
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Payal Singh 6 years, 10 months ago
By Avogadro's hypothesis, the actual volume occupied by the atoms in one gram of a substance is 2/3rd of the volume occupied by 1 gram of the substance.
Let us consider a sample of a substance of mass m and volume V. If M is its molecular weight and Avogadro number is N, then
Number of atoms in the given sample = {tex}{N\over M}× m = {Nm\over M}{/tex}
let each atom is a sphere of radius r..
So
Actual volume of the atoms in the given sample = {tex}{Nm\over M}×{4\over 3}\pi r^3{/tex}
By Avogadro's hypothesis
{tex}{Nm\over M}×{4\over 3}\pi r^3 = {2\over 3}V{/tex}
If {tex}\rho{/tex} is density of substance . Then
{tex}\rho = {m\over V} \\=> V = {m\over \rho}{/tex}
{tex}=> {Nm\over M}×{4\over 3}\pi r^3 = {2\over 3}{m\over \rho}{/tex}
{tex}r = \left ({M\over 2 \pi N\rho }\right )^{1\over 3}{/tex}
Knowing values of M,N and {tex}\rho{/tex}
We can find radius
2Thank You