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\tGive a method to measure size of the atom using Avogadro’s hypothesis?\xa0 |
| Answer» 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, thenNumber of atoms in the given sample =\xa0{tex}{N\\over M}× m = {Nm\\over M}{/tex}let each atom is a sphere of radius r..So\xa0Actual volume of the atoms in the given sample =\xa0{tex}{Nm\\over M}×{4\\over 3}\\pi r^3{/tex}\xa0By Avogadro\'s hypothesis{tex}{Nm\\over M}×{4\\over 3}\\pi r^3 = {2\\over 3}V{/tex}If\xa0{tex}\\rho{/tex}\xa0is 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\xa0{tex}\\rho{/tex}We can find radius\xa0 | |