The answer is it will be remain unchanged.

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.( where Na1 is new avogardo’s number and Na is old avogardro’s number) And we know that mass of one mole of substance is = Na x amu So new atomic mass= Na1 x amu1 = Na/2 x 2amu = Na x amu = old atomic weight.