So, now

$N _{ A } 1$ (avogadro's number) becomes half $( N / 2)$ since the weight of carbon corresponding to a becomes $6 \,gm$ in place of $12$. ( where $N _{ A } 1$ is new avogardo's number and $N _{ A }$ is old avogardro's number)

And we know that mass of one mole of substance is $= N _{ A } \times\, amu$

So new atomic mass $= N _{ A } 1 \times\, amu\,1= N _{ A } \,2 \times\, 2\, amu = N _{ A } \times\, amu \,=$ old atomic weight.