how avogadro discover avogadro's number?
The first measurements which could give an approximate value for Avogadro's number were observations of brownian motion by Robert Brown in 1827.
Cannizarro (1860) used the Avogadro's hypothesis to develop a defensible set of atomic weights based on 1/16 of the atomic weight of oxygen. This was the basis for progressively more accurate estimates for Avogadro's number over the next 100 years. Reasonable values were available in the late 1800's from sedimentation equilibria of colloidal particles. Millikan's oil drop experiment in the early 1900's gave improved accuracy and was cited in most chemistry text books 50 years ago. Text books in 1958 gave Avogadro's number as 6.02 times 10 to the 23rd. The current value is 6.022137 times 10 to the 23rd.
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