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.