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This is because when you consider 1/6 in place of 1/12, since mass of carbon atom is still the same, new amu1 = 2amu ( where amu1 is new amu unit and amu is old amu unit) So now Na1 (avogadro's number) becomes half ( Na/2) since the weight of carbon corresponding to atomic weight becomes 6gm in place of 12.
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