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What were the units used for expressing ...

What were the units used for expressing atomic masses of elements initially ?

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The atomic mass of an element is the weighted average of the atomic masses of different isotopes of that element .This explains,why atomic masses of many elements show large departures from integer values.However ,even if we consider msases of individual isotpes,they are not strictly integer multiples of the mass of a hydroen atom.How do yo account for this fact?